David Cameron is facing a major revolt by the Conservative Party grassroots over his policy on Europe, according to a survey for The Independent.

The poll of 2,205 Tory members by the ConservativeHome.com website found that more than eight in 10 want him to call a referendum on the Treaty of Lisbon even if it has been approved by the next general election – a pledge he is refusing to make.

Total withdrawal from the European Union is the most favoured option among party members when asked how a Tory government should handle the issue, putting them totally at odds with a Tory leadership committed to British membership. Some 82 per cent want to freeze Britain's financial contributions to the EU.

Download the new Independent Premium app Sharing the full story, not just the headlines

The findings suggest that the damaging divisions on Europe which destabilised the last Tory government could resurface at the party's annual conference in Manchester. Mr Cameron has played down the issue but it is firmly back on the agenda because of yesterday's referendum on the Lisbon Treaty in Ireland, the result of which will be announced today. The expected Yes vote would remove the biggest remaining hurdle to ratification by all 27 EU member states. Mr Cameron has promised a referendum in Britain if he becomes prime minister and the treaty has not been ratified by then. But he is reluctant to call one if it has already won EU-wide approval, as withdrawing from it would plunge Britain's relations with its EU partners into chaos.

Conservative Eurosceptics will demand a referendum even if Ireland votes Yes. Mr Cameron will play for time, arguing that the treaty still needs approval by Poland and the Czech Republic. Although he would "not let matters rest" if the treaty has been approved throughout Europe when the election is held, he refuses to say what that means.

Tory MPs believe his approach will come under severe strain if the party wins. Many share the Euroscepticism of the party grassroots highlighted by ConservativeHome's online survey this week. Asked to outline Britain's ideal relationship with the EU, 39 per cent of Tory members believe it should pull out and set up a free trade deal with other European countries. A further 29 per cent say it should remain an EU member but seek a fundamental renegotiation of Britain's terms. Another 20 per cent want to repatriate some powers from Brussels. Only 9 per cent want to stay in the EU and oppose a further loss of sovereignty. In a sign of how far the Tories have shifted on Europe, a tiny 3 per cent of party members say Britain should play a full part in building an "ever closer union".

More than half (55 per cent) want to start a new referendum process if the Lisbon Treaty has been approved and the Tories win power, while 29 per cent say the treaty should be declared illegitimate and a British referendum held to give a Cameron government the authority to opt out of the treaty's provisions. Only 11 per cent of Tory members would accept that the treaty could not be undone – Mr Cameron's likely stance as prime minister – while only 5 per cent would welcome it and put Britain "at the heart of Europe".

Mr Cameron is also under pressure from Tory members to outline a clearer policy on the economy. Some 46 per cent say the Opposition should give specific examples of public services that would be cut and of some taxes that would rise. A further 12 per cent say that the Tories should spell out exactly what would be cut and which taxes would rise. But 42 per cent believe the party cannot set out precise plans until it takes office.

If Mr Cameron were to fall under the proverbial bus, the former leader William Hague (59 per cent) is the overwhelming favourite to succeed him. David Davis, now on the Tory back benches, is favoured by 17 per cent, ahead of the London Mayor Boris Johnson (7 per cent), the shadow Defence Secretary Liam Fox (5 per cent) and the shadow Education Secretary Michael Gove (3 per cent). The shadow Chancellor George Osborne is backed by a surprisingly low 2 per cent, the same proportion which favours the culture spokesman Jeremy Hunt.

Mr Osborne is the third most popular member of Mr Cameron's Shadow Cabinet among party members. He enjoys a net satisfaction rating of 61 per cent (down from 70 per cent a year ago). Mr Hague keeps his place at the top of the popularity chart (83 per cent), while Mr Fox (61 per cent) moves up from seventh to second place. Eric Pickles, the Tory chairman (49 per cent), drops from second to eighth place, while the shadow Home Secretary Chris Grayling (50 per cent) slips from fourth to seventh.