Mrs Merkel arrived in London for dinner with Mr Cameron in Downing Street last night, after contradicting those who think Britain would be better off outside the EU.
"You can be very happy on an island, but being alone in this world doesn't make you any happier," she said.
An increasing number of Tory MPs, including ministers, are asking whether Britain should consider leaving the EU, a suggestion Mr Cameron has rejected.
Speaking to the European Parliament in Brussels before flying to London, Mrs Merkel evoked Britain's role in the Second World War to argue that the UK must remain part of the EU. "I want to have a strong UK in the EU, let me make that absolutely clear," she said.
"I come from Germany. The UK was with us when we were liberated from National Socialism, we still have British soldiers in Germany. I will do everything to keep the UK in the EU as a good partner, that is why I am going to London."
Britain and Germany are two of the biggest contributors to the EU budget, and both are seeking to curb spending in Brussels.
However, the issue has added to tensions between Mrs Merkel and Mr Cameron before a summit on the EU budget for 2014 to 2020, later this month.
The European Commission has asked for an 11 per cent increase in spending, which would take the EU's seven–year spending programme to more than a trillion euros. Mr Cameron wants to reduce the increase by more than £160bn. Mrs Merkel is angry that he has publicly threatened to veto any agreement unless he gets his way.
German sources said the chancellor feared the EU breaking up as Britain moved away from a more closely integrated eurozone.
"In the medium term, it is Britain, a major country, that poses the greatest threat of a schism," said a German official. "Not only is Britain moving away from the EU, but also the EU is moving away from Britain.
By Bruno Waterfield Telegraph.co.uk