David Cameron is facing pressure from Conservative MPs to lurch to the right following his party's disastrous results in the local elections.

In a catastrophic night for the Coalition, the Tories lost 400 seats and the Liberal Democrats 300, leaving Deputy Prime Minister Nick Clegg's footsoldiers with the lowest number of councillors since the party was formed in 1988.

Tory backbenchers urged the Prime Minister to abandon what they see as unnecessary policies – including on gay marriage and Lords reform, both LibDem key aims. They want Mr Cameron to concentrate on more traditional Tory issues, such as creating jobs and sorting out the faltering economy.

The pressure on the Conservative leader was only enhanced by a resurgence in Labour's vote, two years after it lost the General Election.

Ed Miliband declared Labour "back" as he celebrated wins across the UK, culminating in his party taking more than 800 council seats.

Mr Clegg, publicly appeared to face less criticism from his own party than Mr Cameron, although one senior member called on the LibDems to be a "bit more spiky".

The LibDems expected they would receive a hammering in these elections.

But, until a few weeks ago, the Tories had hoped to escape relatively unscathed in England and Wales. Instead, the party suffered a catastrophic set of results, losing swathes of seats and control of 10 councils including Plymouth.

There was also concern that UKIP polled about 13% of the votes in seats it contested, mostly at the expense of the Conservatives.

Both the Tory and the LibDem leaders blamed the tough economic climate for their losses. Mr Cameron said his party had to "take difficult decisions to deal with the debt, deficit and broken economy that we've inherited and we will go on making those decisions".

Tensions erupted between the Coalition partners ahead of the expected renewal of their "marriage" vows, made two years ago next week.

Outspoken Conservative backbencher Peter Bone declared the local election results "the beginning of the end of the Coalition".

Former ministerial aide, Stewart Jackson said: "David Cameron, I think, is on notice that he does need to raise his game. He needs to concentrate on bread and butter issues – like jobs and mortgages and public services, and above all develop a clear route map to growth – and stop fixating on the agenda of a liberal clique and barmy policies such as Lords reform and gay marriage."

Although expected, the results are a blow to the LibDems. The party will be aware of how much it depends on grassroots campaigners in the run-up to general elections.

One senior LibDem put the Coalition's trouncing down in part to last month's Budget cut in the top rate of tax from 50p to 45p.

LibDem deputy leader Simon Hughes said the move did "far more damage than anything else" to his party.

However, he also suggested that it hurt the Tories as well, leaving them open to accusation of orchestrating a tax cut for millionaires.

"If [the Coalition] hadn't done that, the Tories wouldn't have done so badly and we wouldn't have done so badly," he said.