After the Tories suffered heavy losses to the UK Independence Party in the council elections, Mrs May said it was essential voters believed the party would honour its promise to hold an in/out referendum on EU membership after the next general election.
However she rejected calls from some senior Conservatives to bring forward the date of the referendum and stage it in this parliament in order to finally kill off the appeal of Ukip to Tory voters.
She said that it was important that they stood by David Cameron's plan to re-negotiate the terms of Britain's membership and then put the new settlement to the country.
"If you want to take a re-negotiated settlement to the British people, you have got to re-negotiate it," she told the BBC Radio 4 Today.
More top news
Ed Miliband is demanding the Conservatives must "come clean" over their plans for the NHS amid claims of greater privatisation
Thousands of Ethiopian Jews have taken to the streets of Tel Aviv to protest against racism and police brutality
Temperatures will be on the warm side tomorrow as much of the country looks forward to a fine bright start to the day.