* Merkel wants a "strong GB inside the European Union"
* German and British leaders discuss EU budget in London
* Cameron opposes "ludicrous" budget rise
By Peter Griffiths and Claire Davenport
LONDON, Nov 7 (Reuters) - Germany's Angela Merkel on Wednesday warned Britain not to turn its back on Europe and urged its Prime Minister David Cameron to work with her to avoid deadlock at European Union budget talks later this month.
The leaders met in London to try to iron out differences over the EU's 1 trillion euro ($1.28 trillion) budget that threaten to block a deal and fuel fears that London is drifting away from the 27-nation union..
Describing plans to increase the EU budget as "ludicrous", Cameron has threatened to veto any deal he thinks is not in Britain's interests and will push for a real-terms freeze.
However, German officials are exasperated by what they see as London's slide towards Europe's margins, a feeling reinforced last week after the British parliament voted to call for a real-terms cut in the EU's budget.
Before meeting Cameron, the German Chancellor told the European Parliament she could not imagine a Europe without Britain, the world's sixth largest economy, which relies on the EU for half its trade.
"I believe you can be very happy on an island, but being alone in this world doesn't make you any happier," Merkel said after British politician Nigel Farage, leader of the anti-European UK Independence Party, urged her to tell Cameron that Britain should quit the EU.
Cameron, who wants to stay in the bloc under renegotiated terms, argues that the EU must tighten its belt at a time when the euro zone debt crisis looms large, and many countries are faced with austerity and shrinking household budgets.
"They are proposing a completely ludicrous 100 billion euro increase," Cameron said. "I never had very high hopes for a November agreement because you have got 27 different people round the table with 27 different opinions."
Cameron was humiliated by last week's defeat in parliament and opponents say he has lost control of Conservative Party anti-Europeans, a group that helped topple former leaders and that wants a referendum on Britain's EU membership.
Debate over a referendum on Britain reworking its EU role or even leaving has climbed the agenda. A YouGov survey in October found 49 percent of those polled wanted to leave the EU, against 28 percent who wanted to stay in it.
Talking tough on Europe can play well with "eurosceptic" British voters and Conservative politicians, but Cameron risks angering EU neighbours and his pro-European coalition partners, the Liberal Democrats.
Merkel acknowledged the need to keep domestic opinion on side during the budget negotiations.
"We always have to do something that will stand up to public opinion back home," she told reporters, adding that the EU must address areas where money is wasted. "Despite differences that we have, it is very important for me that the UK and Germany work together."
Cameron's threat to block a deal could delay a funding increase for the poorest east European member states and isolate Britain from disgruntled EU nations. He has already angered some by talking of using closer euro zone integration as a chance to repatriate some powers from Brussels.
France and Denmark have also threatened to block a budget deal to press their own interests, highlighting the obstacle course facing EU leaders.
Germany is the biggest net contributor to the budget while Britain, which receives an annual rebate on its payments, is the fourth largest net payer after France and Italy.