David Cameron is under fresh pressure from both sides of the house to call an EU referendum before the election, as the prominent Labour MP Tom Watson joined a Tory campaign for an early vote.

Watson, a former Labour minister and campaign director, said he was planning to support Adam Afriyie, a Tory backbencher, who is leading calls for an in-out poll before 2015.

The move has been firmly rebuffed by No 10, which said the prime minister would in no circumstances allow a referendum before he had had a chance to renegotiate Britain's relationship with EU. Cameron is supporting a bill by James Wharton, a backbencher, which sets out a plan to hold a referendum before the end of 2017.

However, Afriyie is not satisfied with this timetable, arguing that voters are suspicious that they are not being allowed to have a say on Britain's EU membership straight away. He is planning to table an amendment to Wharton's bill calling for a referendum on 23 October 2014.

The Windsor MP has been the subject of speculation that he would like to be leader of the Conservative party. Speaking on Sky News's Murnaghan programme, he said it was "media tittle-tattle" that he wanted to succeed Cameron and insisted he was loyal to the leadership, but said he could not "sit quietly" while the referendum was put off until 2017.

Watson added fuel to the row by saying "a lot of people" in both Labour and the Conservatives wanted a referendum sooner.

"I don't want to add to the PM's panic, but I will probably be supporting Adam Afriyie with his amendment," he told the BBC's Andrew Marr Show.

"I think there are a lot of people on both sides of the house who think we need clarity on this now. The country has asked for it for a long time, business has been saying there's a lot of uncertainty and parties have got to draw up their manifestos for the 2015 general election and they will be very difficult, depending on the outcome of a referendum."

Watson's move will also add to pressure on Ed Miliband, the Labour leader, who has not yet made it clear his views on a vote.

"He's kept his options open. He's said he will take that decision at a later date, but I just don't know," Watson said. "It would be down to him and Douglas Alexander but now I'm on the backbenches, I think I might support Adam."

A number of Tories argue an early EU referendum would stop voters turning to the UK Independence party in 2015 if they do not believe Cameron will stick to his promise after the election.

Afriyie claims delaying a poll poses "significant dangers", including building support for Ukip, and argues he has the support of "many MPs from across all the main parties" for an early referendum.

"It's in our national interest to resolve this issue as soon as possible to create the certainty and stability our country needs for the future," he wrote in the Mail on Sunday.

"Only by setting an early date can we kickstart EU renegotiation talks and give the British people what they so clearly want – a say on our country's future with Europe.

"The political establishment are naturally hesitant but we have nothing to fear by giving people a chance to have their say, either way, on our future relationship with Europe."

Questioning Cameron's tactics, he wrote: "The fact is, the British people are not convinced there will be a referendum at all if we wait until after the next general election.

"So many things can change. They don't understand why we can't have one right away – and that makes them suspicious.

"Many people think delaying the vote is just a tactic to allow all the political leaders to kick the can even further down the road.

"In reality, the British people are unsure whether the Conservative leadership would be able to stick to its promise of holding a referendum after the election, especially if in coalition once again."

Despite his protestations of loyalty, Afriyie's move is being seen as a challenge to Cameron's authority.

Speaking on the BBC's Marr Show, Nigel Farage, the Ukip leader, dismissed the prime minister's promise of a poll before 2017 as a way of "kicking the issue into the long grass".

However, Theresa May, the home secretary, defended the government's plans, saying Cameron was planning a "serious negotiation" before taking the option of a new settlement to the British people.

The European Union (referendum) bill easily cleared its first Commons hurdle in July after Labour and the Liberal Democrats avoided voting on the issue.

Wharton said the rebel amendment would "make it far more difficult to navigate the challenging procedural hurdles we need to overcome and I hope its sponsors might rethink their approach".

"We need to build as broad a base of support for the bill as we can if we are to get it through parliament and the policy of a renegotiation, followed by an in-out referendum, is the right one to do that and the right one for the country.

"I hope MPs will decline to support it as the ultimate impact might well be to kill my bill, which would only help those who don't want any referendum at all."

Ed Miliband and Nick Clegg have dismissed the bill as a stunt designed to shore up the prime minister's position with his rank and file – pointing out that it has virtually no chance of becoming law.

In May, 115 Conservative MPs backed a rebel amendment to the Queen's speech criticising the failure to include a referendum bill in the government's legislative programme.

Cameron said that was impossible because of being in coalition with the pro-European Lib Dems, but has thrown his weight behind Wharton's bill.