Topping Pool 2 may have meant Edinburgh avoided a trip to Dublin's Aviva Stadium in the Heineken Cup quarter-finals but they look certain to have to visit Ireland's national stadium if they are to reach the final at Twickenham in May.

The draw for the semi-finals was made immediately after an epic afternoon's rugby saw Edinburgh and Cardiff Blues take the Celtic contingent to five, the first time any one league has so dominated the pool stages of the competition.

The winners of the Edinburgh v Toulouse match will consequently face a visit to Ireland to face either Munster or Ulster. Regardless of which club they face, demand for tickets will almost certainly lead the fixture to be moved to the Aviva Stadium.

Playing there in a semi-final against either province would surely be a less daunting prospect, however, than having to face defending champions Leinster in their home city. That prospect was facing Edinburgh until they secured a bonus point with their fourth try that took them above Cardiff while transforming them into third seeds, earning a home quarter-final against Toulouse.

While delighted with the overall outcome Michael Bradley, Edinburgh's head coach, was not prepared to look ahead to a return to his native Ireland, though.

"I think we'll get over Toulouse first and we'll worry about the winner of that game after," he said. "That will be a great game actually, Ulster v Munster. Ulster are coming into form as we saw here. We put in a disappointing performance against them, but that was put into perspective by what they did to Leicester and also what they did against Clermont, so they will go into that match with a lot of confidence."

That is partly down to having faced each other regularly. The Scottish teams should be drawing similar belief from knowing they are playing in what is by far the strongest domestic league in European rugby.

Result after result has demonstrated that in this season's Heineken Cup and, in particular, the record of Celtic teams against opposition from the over-hyped English Premiership demonstrates just how much power has shifted within the British and European game.

This season's pool stages have only reinforced the message delivered by Munster and Leinster, who have claimed four Heineken Cups between them in the last six years while English and French clubs have won just one apiece.

This season's tournament began with just one Celtic team losing on the first weekend and they also finished strongly with Connacht – by far the weakest of the Celtic competitors as they took part in Europe's top competition for the first time – shocking English Premiership leaders Harlequins on the opening night of the competition.

That was followed up in spectacular fashion on Saturday when all the talk from English pundits had been about how determined Northampton Saints, last season's beaten finalists, were to take revenge on Munster following the last-gasp defeat the suffered in Limerick on the opening weekend.

Level at the interval, they were given a rugby lesson in the second half as the two-time champions passed the half-century mark. Leicester fared only a little better the previous week, Ulster only thrashing them 41-7. Similarly at Murrayfield yesterday, there were claims that London Irish would spoil Edinburgh's big day before they, too, were comprehensively outplayed.

The right note of respect for both Celtic rugby and Edinburgh was, however, struck by the most successful coach in the competition's history when Guy Noves, who has steered Toulouse to six finals and four title wins looked ahead to his side's impending visit to Murrayfield.

"Edinburgh are a complete team," said Noves. "I watched Edinburgh as a classic spectator during the pool games. Especially during the game [against] Racing Metro in Paris, they were impressive, a complete rugby team.

"People think that Edinburgh have good backs but lack power with their forwards, but I disagree with that. When they played against the Racing Metro they had a good continuity and went through the phases and were very good at turnovers, and believe me Racing have very powerful forwards.

"People see Toulouse as a team which play open and attacking rugby and are very dynamic but we, like Edinburgh, have good continuity and go through the phases.

"Edinburgh really represent Scottish rugby well which is actually in a positive time at the moment. They have got better and better the last few years. I watched the game against London Irish without thinking that we could play against them in the quarter-finals, but now I will have to study them closer."

Topping Pool 2 may have meant Edinburgh avoided a trip to Dublin's Aviva Stadium in the Heineken Cup quarter-finals but they look certain to have to visit Ireland's national stadium if they are to reach the final at Twickenham in May.

The draw for the semi-finals was made immediately after an epic afternoon's rugby saw Edinburgh and Cardiff Blues take the Celtic contingent to five, the first time any one league has so dominated the pool stages of the competition.

The winners of the Edinburgh v Toulouse match will consequently face a visit to Ireland to face either Munster or Ulster. Regardless of which club they face, demand for tickets will almost certainly lead the fixture to be moved to the Aviva Stadium.

Playing there in a semi-final against either province would surely be a less daunting prospect, however, than having to face defending champions Leinster in their home city. That prospect was facing Edinburgh until they secured a bonus point with their fourth try that took them above Cardiff while transforming them into third seeds, earning a home quarter-final against Toulouse.

While delighted with the overall outcome Michael Bradley, Edinburgh's head coach, was not prepared to look ahead to a return to his native Ireland, though.

"I think we'll get over Toulouse first and we'll worry about the winner of that game after," he said. "That will be a great game actually, Ulster v Munster. Ulster are coming into form as we saw here. We put in a disappointing performance against them, but that was put into perspective by what they did to Leicester and also what they did against Clermont, so they will go into that match with a lot of confidence."

That is partly down to having faced each other regularly. The Scottish teams should be drawing similar belief from knowing they are playing in what is by far the strongest domestic league in European rugby.

Result after result has demonstrated that in this season's Heineken Cup and, in particular, the record of Celtic teams against opposition from the over-hyped English Premiership demonstrates just how much power has shifted within the British and European game.

This season's pool stages have only reinforced the message delivered by Munster and Leinster, who have claimed four Heineken Cups between them in the last six years while English and French clubs have won just one apiece.

This season's tournament began with just one Celtic team losing on the first weekend and they also finished strongly with Connacht – by far the weakest of the Celtic competitors as they took part in Europe's top competition for the first time – shocking English Premiership leaders Harlequins on the opening night of the competition.

That was followed up in spectacular fashion on Saturday when all the talk from English pundits had been about how determined Northampton Saints, last season's beaten finalists, were to take revenge on Munster following the last-gasp defeat the suffered in Limerick on the opening weekend.

Level at the interval, they were given a rugby lesson in the second half as the two-time champions passed the half-century mark. Leicester fared only a little better the previous week, Ulster only thrashing them 41-7. Similarly at Murrayfield yesterday, there were claims that London Irish would spoil Edinburgh's big day before they, too, were comprehensively outplayed.

The right note of respect for both Celtic rugby and Edinburgh was, however, struck by the most successful coach in the competition's history when Guy Noves, who has steered Toulouse to six finals and four title wins looked ahead to his side's impending visit to Murrayfield.

"Edinburgh are a complete team," said Noves. "I watched Edinburgh as a classic spectator during the pool games. Especially during the game [against] Racing Metro in Paris, they were impressive, a complete rugby team.

"People think that Edinburgh have good backs but lack power with their forwards, but I disagree with that. When they played against the Racing Metro they had a good continuity and went through the phases and were very good at turnovers, and believe me Racing have very powerful forwards.

"People see Toulouse as a team which play open and attacking rugby and are very dynamic but we, like Edinburgh, have good continuity and go through the phases.

"Edinburgh really represent Scottish rugby well which is actually in a positive time at the moment. They have got better and better the last few years. I watched the game against London Irish without thinking that we could play against them in the quarter-finals, but now I will have to study them closer."