IT might be viewed as an unlikely consequence but it seems Christmas dinner chez the Murrays has caused indigestion for the tennis authorities.

Andy Murray has become the latest of the clan to question the strategy of those who run the sport in Britain.

His strongest intervention came after he had beaten John Isner to take Great Britain through to a semi-final of the Davis Cup. Murray was keen to emphasise, though, that the future of tennis depends more on participation at a lower level than success at a higher level.

The Murray Factor has grown stronger over a decade but the 27-year-old Scot seems dissatisfied about how it is being exploited.

The Wimbledon champion was asked in the immediate aftermath of his historic victory on Sunday at the Emirates Arena if he had been tapped for any input into the strategy to take British tennis forward. He replied that he had a 15-minute chat with Michael Downey, the chief executive of the Lawn Tennis Association, that morning.

His reflection on the extraordinary atmosphere at Braehead was telling. "You see the enthusiasm and the passion that people clearly have for tennis right now. That's great. It's up to the LTA to capitalise on that. That's not my job," he said.

Murray spoke last week of how the family had discussed the state of tennis at Christmas and they have not kept their conclusions to themselves. Judy Murray told The Herald last week of her fears that the Murray window of opportunity could be closed without the extraordinary success of both her sons being built upon.

Jamie Murray was even more blunt in a newspaper interview, insisting the LTA neglected Scotland and was scathing about Tennis Scotland.

Murray the younger supported his mother and brother at a pre-match Davis Cup press conference by saying he respected their views.

He was more forthcoming as he sat in a hall in the Emirates, drained by the emotion of a compelling contest but sharp enough to make his points off-court.

His most devastating response was to confirm that the 15-minute natter at the Emirates was his longest conversation with Downey. The Canadian was appointed in September 2013.

He said of the chat on Sunday: "He sort of took me through a one-page plan, strategy, in terms of how they were going to get more people playing the game.

"I haven't given my opinion or thoughts on how that should be done. I just listened to what he had to say.

"Getting more people playing is obviously important. The more people we have playing, the more chance we have to get more top players."

And how is this for the clincher?

"But it's one thing saying it, putting it down on a piece of paper. It's another thing doing it, actually following through with it. We'll have to wait and see."

One hesitates to peer behind the words but it is surely reasonable to accept that the Murray family is not enamoured with the application of strategy or even the intellectual rigour behind it.

The new deal from the LTA gives Tennis Scotland £3.3m a year for four years. Jamie Murray has already questioned if this is enough, given that the LTA takes £35m a year from Wimbledon.

There is no question about the appetite for tennis, particularly in Scotland. More than 20,000 people made the tie at the Emirates a sell-out over three days. It is impossible to be precise but it is reasonable to propose that a Davis Cup semi-final against France in July would sell-out any 10,000 arena in Scotland on all three days.

Murray and his family are aware of this unprecedented level of interest and are dismayed that it is not being exploited in terms of surging participation figures and the building of indoor courts.

The Wimbledon was diplomatic over the impact of the Davis Cup success but straightforward on who should take on the burden of ensuring on this golden era if followed by yet another.

" I'm just happy that when we've been able to play the big events of the last few years, the crowds have been absolutely fantastic every time. Again in the summer I'm sure we can fill another big arena.

"But we need more than just putting these sort of events on. It's the LTA's job to capitalise on the interest that's around just now."

Murray's personal strategy is to build on a start to the season that has been very encouraging. The Australian Open final has been followed by a Davis Cup quarter-final where he won two points by outclassing Donald Young and then withstanding the big-serving Isner with a mixture of technique, indefatigable retrieving and mental strength.

A sign of Murray's resilience and capacity for defying heavy artillery came in when it took the 6ft10ns Isner six aces to win one game.

The Scot now seeks to take his form to Indian Wells for a run that includes the first Masters series events of the season and then the clay court campaign that culminates at Roland Garros in May.

He has now risen to No.4 in the world and is close to appointing a travelling coach to supplement Amelie Mauresmo. "I'll try to arrange someone to do a trial week or trial period in the next month or so," he said.

His schedule is slightly complicated by his marriage to Kim Sears at Cromlix Hotel next month. But his ambitions are clear.

Murray seeks a grand slam title this to add to the two he has already won. His initial tilt will come on foreign fields but no one should doubt he will keep an eye on developments or otherwise at home.