A YouGov poll of nearly 1,300 people for The Sunday Times shows that voters would reject the new constitution by 49% to 23%. Another poll, carried out by ICM for the cross-party Vote No campaign, shows 57% to 28% opposition to the constitution.

It also shows that voters are sceptical about the prime minister’s assurances that Britain will retain complete control over taxes, defence, criminal justice and asylum policy. By 64% to 28% people believe sovereignty will be ceded in some or all of these areas.

Opposition politicians and business leaders said the deal Britain had negotiated would see the European Court of Justice called in to judge on key national matters.

The prime minister hailed the deal late on Friday night as a victory for Britain’s interests. But as the dust settled yesterday there was concern, particularly over the charter of fundamental human rights.

Digby Jones, director-general of the CBI, said that parts of the deal were “very worrying”.

He feared that workers and trade unions would be able to challenge employers under the charter by using the European court. “Pro-integrationist decisions by the European Court of Justice in the fields of tax and labour law remain a serious threat to UK competitiveness,” Jones said.

“Sadly, this constitution does nothing to make Europe more globally competitive and the jobs of millions deserve more from this document.”

The phrasing of the agreement on the charter says that “it will be interpreted by the courts of the union and the member states”. Opponents say that leaves the way open for the European Court of Justice to play a key role, crossing into domestic labour laws.

The Sunday Times-YouGov poll reveals widespread ignorance about the constitution. Many people wrongly believe that it gives Europe immediate power to control tax rates in Britain, that a European passport will replace the British one, that Britain will need EU approval before fighting a war and that a European representative will replace Britain on the United Nations security council.

If all their concerns on these and other issues were met, voters said they would back the constitution by 41% to 35%. But this is likely to be of only small comfort to Blair. On asylum, the one key issue where control has been handed over, there is widespread public disquiet. The ICM poll shows that by 55% to 23% people would reject the constitution even if it meant that Blair would have to resign.

The Vote No campaign will relaunch this week and yesterday unveiled a number of big business backers. They include Sir Rocco Forte, the hotelier, Michael Spencer, chairman of the money broker Icap, Simon Wolfson, chief executive of Next, the fashion chain, Roger Bootle, the economist, and Sir Crispin David, chief executive of Reed Elsevier, the publisher.

A referendum in Britain is not likely before 2006, but the Vote No campaign has already built a war chest of several million pounds. Tomorrow Blair will face tough questioning in the Commons. Michael Howard, the Tory leader, is expected to challenge him to hold a quick referendum.

Michael Ancram, the shadow foreign secretary, said: “In a sly way this constitution strips power from Britain by the growing control it gives European judges. They will interpret the new supremacy of the constitution over our own constitution, laws and courts. It must be exposed and opposed.”

Under the constitution the European parliament and the union will have a greater role in tackling international crime and on asylum and immigration policy. Last night Sir Andrew Green, chairman of Migrationwatch UK, said: “This is a disaster. It locks us into a failed international convention (on refugees) and removes our autonomy in deciding how to manage an issue critical to our future.”

Denis MacShane, the Europe minister, said: “The charter enshrines core British and European values. It is wrong to say it sees French, German or English industrial laws rewritten. They will still be decided nationally.”

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