Nick Clegg has told the SNP to get off his party's turf, as he hit back after Alex Salmond linked home rule to independence.

The LibDem Deputy Prime Minister's criticism came during a keynote speech at the end of his party's spring conference in Gateshead yesterday.

It followed the First Minister telling the SNP's own gathering in Glasgow that "home rule with independence beats Tory home rule from Westminster".

The LibDems have taken issue with his use of the term – insisting it had nothing to do with leaving the UK.

Mr Clegg told delegates that they were the "party of home rule", adding: "Alex Salmond wants to break up the nations of the UK, I want to keep us together. He says it is time for division – I say it is time for unity".

He told party members they had to join together to "fight the forces of division".

Pete Wishart, the SNP's Constitutional Affairs spokesman, said Mr Clegg's remarks meant the public could now see the LibDems were the party of "Tory rule – not home rule".

He added: "If Nick Clegg genuinely wanted to deliver the powers that people in Scotland want for the Scottish Parliament he could do it right now by improving the Scotland Bill."

Mr Salmond's language has antagonised the LibDems, who back home rule as a long-term commitment to further devolution, but one that rejects independence.

Last year, Scottish LibDem leader Willie Rennie set up a new party commission to look at Home Rule, headed by Sir Menzies Campbell, to assess what extra powers for Scotland might mean.

Scottish LibDem president Malcolm Bruce accused Mr Salmond of "trying to deliberately confuse people".

He added: "Independence and home rule are two completely different things. We know that is the case because the SNP have heaped scorn on home rule for decades."

Mr Clegg also used his speech to take a broadside at a senior member of his own party, as tensions soured within the LibDems over competing tax plans. It came just hours after the millionaire Lord Oakeshott, who is close to Business Secretary Vince Cable, accused the leader of making up policy "on the hoof".

To laughter from delegates, Mr Clegg said that the "one person" who objected to the idea was one of the party's own tycoons.

The Business Secretary is backing calls for a mansion tax on those with homes worth more than £2 million. His speech to conference on Saturday was widely interpreted as a retrenchment of his position, and in an interview Mr Cable admitted he had not "seen the detail" of Mr Clegg's plan.

Danny Alexander also appeared to pour cold water on the idea when he described it as "one of a number" being considered ahead of the Budget, now less than a fortnight away.

However, sources close to Mr Clegg insisted yesterday that the Tycoon Tax principle was part of a discussion taking place ahead of the Chancellor's statement on March 21.

The LibDem leader also used his speech to say that the Budget must include faster moves to raise the tax threshold for those on low wages, and to pledge that the Coalition's controversial House of Lords reform would happen, saying there would be elections to the Upper Chamber by 2015.

He made an early play for re-election, saying the party would still have much it wanted to achieve. He also told rank-and-file members that he had not become the part of the establishment in Government and was as "radical" as ever.

There was also a tribute to Chris Huhne, the former energy secretary, who stood down last month after he was charged over allegations he asked his wife to accept his penalty points for speeding.