The number of lawmakers in Prime Minister David Cameron's party to join a group pushing for Britain to leave the European Union unless it obtains major changes to its terms of membership has jumped from 50 to 110 in a week, a newspaper said on Saturday.

One in three of Cameron's 330 lawmakers, including some ministers, have joined "Conservatives for Britain" (CfB), which is also backed by 13 members of the upper house and 12 members of the European Parliament, the Telegraph reported.

Last weekend, the paper said the group had just over 50 members.

CfB backs Cameron's efforts to renegotiate Britain's relationship with the EU but will push to leave the 28-member bloc if "drastic changes" are not secured, according to the centre-right Telegraph.

Britain's Conservatives won an unexpected, but slim, parliamentary majority at elections last month, and promised to hold an "in/out" referendum on EU membership by the end of 2017.

Cameron has since toured European capitals seeking to drum up support for reforms including being able to limit welfare payments to workers coming to Britain from other EU countries.

Steve Baker, the member of parliament who heads the CfB, said a significant proportion of its members believed Cameron would be able to reach an acceptable agreement.

"About three-fifths think a successful renegotiation is possible and will make a decision when the renegotiated position becomes clear," he was quoted as saying, but added that around one in five thought a satisfactory deal was "unlikely".

The Telegraph said some ministers had joined the group but Baker had declined to reveal their names.

Cameron angered some in his party at the start of the week when he suggested ministers who did not back his EU strategy, which envisions Britain remaining in a reformed EU, would have to quit the government.

He later said he had been misunderstood and that his warning to ministers only applied to the EU negotiation period and not the referendum campaign itself where many Conservatives feel they should be allowed to vote according to their own conscience, rather than following the party line.

The Telegraph said some Eurosceptic Conservatives fear Cameron may try to secure a 'yes' vote by holding it as early as next May in order to limit the time available to debate any deal he reaches with Britain's EU partners.

A spokeswoman at Cameron's office did not offer an immediate comment when contacted by Reuters.