Sutton and Cheam MP Paul Scully claimed the ex-prime minister had made a grave error after he “limited himself” before launching his failed renegotiation of Britain’s EU relationship earlier this year.
Mr Scully suggested Mr Cameron might have avoided his EU referendum humiliation if he had been more ambitious in his initial demands for change from Brussels.
The backbencher used Mr Cameron’s example to urge Mrs May not to spell out a set negotiating position prior to triggering Article 50 of the Lisbon Treaty.
The Prime Minister has vowed to invoke the legal mechanism for quitting the EU before March next year.
Mr Scully spoke in a Westminster Hall debate in Parliament this afternoon as MPs debated a number of official petitions to have attracted support in the wake of the historic Brexit vote on June 23.
Signed by thousands of Remain supporters, one has urged the Government not to trigger Article 50 with another suggesting Parliament itself should decide whether Britain leaves the EU, despite the referendum result.
Speaking in the debate, Labour MP Geraint Davies claimed Article 50 should not be triggered until the EU informs Mrs May of what exit package it will hand Britain.
The Swansea West MP suggested at that point, a second EU referendum should then be held because the deal could be “very different from what people reasonably understood when they made their vote on June 23”.
But Mr Scully hit back, telling Mr Davies the Brexit talks would be an “open negotiation” with the 27 other EU member states squabbling amongst themselves to decide what to offer Britain.
He suggested Germany would be in favour of handing good terms to Britain due to the country’s huge car exports to the UK, even if Jean-Claude Juncker’s European Commission insists on “burying their head in the sand”.
Mr Scully added: “Article 50 actually says we have to take into account our future relationship but I think there is plenty of time. We need to use the full two years in order to work out our future relationship.
“I wouldn”t want to see is us being hamstrung by waiting to invoke Article 50 because we are trying to limit ourselves in our future negotiations over our future relationship with the EU.
“Frankly, from a personal point of view, I think this is what actually hamstrung David Cameron in the first place.
“If he”d asked for more and if he hadn”t limited himself in his renegotiations with the EU earlier on last year, we may be in a very different place in the lead-up to the referendum and we may still have voted to Remain.
“So I don”t want to be in the position now where we are actually limiting ourselves in our negotiations in how we move forward once we”ve left the EU – just to get to this point in time by next March when we”re actually invoking Article 50 and starting the process. “
In February this year, Mr Cameron saw his EU renegotiation derided as ‘feeble’ and ‘watered-down thin gruel’ after he failed to win any curbs to Brussels’ freedom of movement rules.