THE SNP last night seized on the result from the Eastleigh by-election to argue Westminster's politics was becoming increasingly right-wing, Europhobic and alien to Scots voters, and claimed that would boost the case for independence.

Nicola Sturgeon, Deputy First Minister and linchpin of the Yes campaign, said the second-place result for the UK Independence Party in the Hampshire seat, after its negative focus on the EU and immigration, would also push the Tories and Labour further to the right in an attempt to stop Ukip eating into their vote.

Scottish LibDem leader Willie Rennie in turn accused Sturgeon of trying to "demonise" the English.

Eastleigh was held on Thursday by the LibDems despite the previous MP, former energy minister Chris Huhne, resigning after admitting he asked his wife to take his speeding points – an offence that now leaves him facing prison.

The LibDems were also dogged by allegations their former chief executive, Lord Rennard, made unwanted advances to women in the party.

In spite of the murky backdrop, the LibDems' Mike Thornton won the seat, albeit with a hugely reduced majority, coming just 1771 votes ahead of Ukip's Diane James, who increased her party's share of the vote from 4% in 2010 to 28%.

The massive 19.3% swing to Ukip pushed the Conservatives into third, a disaster for David Cameron as Eastleigh was a Tory target seat. Senior Tory MP David Davis had earlier predicted third place would be a "crisis" for the party.

Labour straggled in fourth, suggesting leader Ed Miliband's "One Nation" strategy has yet to convince voters in England's southeast.

But the result was worst for the Prime Minister, with many of his MPs suggesting it showed the party had lost touch with voters' concerns. With Tory MPs already worried about losing the 2015 General Election, some privately warned Cameron could face a leadership challenge unless the party's fortunes start to revive.

Tory right-winger Stewart Jackson, MP for Peterborough, hit out at Cameron and called for immediate change, saying: "Unless things are demonstrably different in terms of public perception by the early summer he will have great difficulty in persuading the electorate we can win a General Election.

"He is out of touch with the party. Both gay marriage and EU migration feed into a narrative that too much emphasis is going to the liberal metropolitan elite and not enough to the blue-collar working vote Margaret Thatcher had the support of."

Sturgeon said: "Eastleigh shows just how far the politics of Westminster has diverged from Scotland – it will boost the siren voices in the Tory Party who want to cut us out of Europe and the single market of half-a-billion people, and those in Labour who want their party also to back a referendum on an EU exit. It reinforces the need for a Yes vote in Scotland's independence referendum, because the decisions of the Westminster system are moving further and further away from the economic and social interests of the people of Scotland.

"While Ukip is dictating policy south of the Border, it has never moved beyond the far fringes of Scottish politics."

Scottish LibDem leader Willie Rennie accused the Nationalists of trying to "demonise" England. He said: "They're trying to demonise the whole of England as being some kind of right wing conglomerate and that's not my experience having lived there for several years. The English are a very compassionate and outward looking people."

Scottish Conservative deputy leader Jackson Carlaw said: "Lessons must always be learned from any by-election and the Scottish Conservatives will reflect carefully. This is something I am sure the SNP has not done following the various defeats it has experienced in recent local government by-elections."

Running counter to Sturgeon's argument is the theory that Eastleigh is actually bad for the Yes campaign, as it makes a Tory win in 2015 look far less likely – and the prospect of a Labour win would undermine the idea of independence as the best way to escape from Tory austerity.

Professor John Curtice of Strathclyde University described the SNP argument as "rubbish". But he said Ukip's rise might yet influence Westminster politics in relation to Scotland.

"Ukip are not very keen on devolution. If they increase pressure on Westminster not to grant Scotland more devolution, then that could cause trouble," he said.