The British premier rolled out the red carpet in his bid to woo fellow conservative Merkel, who gave a speech to both houses of parliament before taking tea with the queen.
But Europe's most powerful politician was cool on Cameron's desire to change the EU's treaties ahead of a planned referendum on British membership of the bloc in 2017.
Merkel said in her speech to parliament that Britain and Germany shared the goal of a "strong and competitive" EU that was a "model for other regions of the world".
However she admitted Cameron might be disappointed by her speech to members of the House of Commons and House of the Lords, the first by a German leader since president Richard von Weizsaecker's address in 1986.
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"I have heard some expect my speech to pave the way for a fundamental reform of European architecture which will satisfy all kinds of alleged or actual British wishes. I am afraid they are in for a disappointment," she said.
Cameron said they discussed ways of cutting "excessive interference and meddling" by Brussels and of protecting member states like Britain that do not use the euro.
"Angela and I both want to see change in Europe and we both believe change is possible," he said.
Merkel offered support for his concerns over EU migrants claiming social benefits, saying that if new arrivals got as much as long-term citizens there will be an "onslaught".
"If one wants Britain to remain in the European Union which is what I want, if one at the same time wants a competitive union that generates growth, one can find common solutions," she said.
She then headed off to have tea at Buckingham Palace with Queen Elizabeth II.
Cameron hopes to win over voters in Britain's in-out referendum by securing reforms that would dilute Europe's influence over domestic policy. He has said the vote will be in late 2017, provided he is re-elected in 2015.
The warm reception given to Merkel contrasted with that accorded to French President Francois Hollande, who had a brief summit at a chilly airfield and a pub lunch with Cameron last month.
Merkel follows in the footsteps of US President Barack Obama and French ex-president Nicolas Sarkozy in speaking to the twin chambers of parliament at Westminster.