George Osborne arrives at 10 Downing Street as Britain's Prime Minister David Cameron begins to appoint his cabinet after securing a majority goverment, in central London, May 8, 2015.[Photo/Agencies]

The Sunday Times said the changes to electoral districts being considered by Cameron could give his Conservative party an extra 20 seats in parliament. They hold 331 of the total 650 seats after Thursday's election.

Cameron is under pressure from within his party to push for big changes to Britain's membership of the EU and some Conservative lawmakers favour an EU exit.

The UK Independence Party (UKIP), which wants Britain out of the EU, won nearly 13 percent of the vote in the election, although it has only one seat in parliament.

An opinion poll published earlier this month showed 34 percent of Britons would definitely vote to remain in the EU, and a further 18 percent would probably vote to stay in. Eighteen percent said they definitely wanted to leave the bloc and 14 percent said they would probably vote to exit.