The help of Germany is key to this process. If Merkel grants any concessions to Cameron on her visit this week, it will be viewed as a triumph by the Conservatives and a strengthening of the North-South power balance in the EU.
"Merkel is trying to keep the Brits on board. They have been very worried about the British moving away from the EU and that Germany would be left alone," Carsten Nickel, senior vice-president at Teneo Intelligence, told CNBC.
(Read more: Slash EU red tape, UK business says)
A closer Anglo-German alliance could re-affirm the old North-South divides and stereotypes in Europe, with Nordic, Anglo-Saxon disciplinarians lined up against the spendthrift southern and Mediterranean members.
It could also help calm Euroskeptic voices within the U.K., which threaten the country's ongoing relationship with the trading bloc.
"At some points, the tone of the domestic debate has been more focused on the requirements of domestic politics than the need to build positive relationships with other member states," Alisdair McIntosh, director of Business New Europe, the pro-EU lobby group, told CNBC.
(Read more: How Brixit could affect U.K.)
Merkel and Cameron agree on the need to make Europe more competitive and the importance of budget discipline.
And the majority of people in both of their countries think that certain issues should be determined at the national rather than EU level, according to a poll by YouGov for campaign group Open Europe released Wednesday.
Germans are generally more pro-EU, with just 9 percent wanting Germany out of the union, compared to 24 percent of the British, the poll suggests.
(Read more: U.K. 'destroying future' over immigration: EU official)
"Germany has already shown itself sympathetic to the U.K.'s concerns," Stephen Booth, research director at Open Europe, told CNBC. The controversy over plans for a single European banking regulator, the European Banking Authority, showed Merkel is "alive to concerns the U.K. may be sidelined," he added.
Despite Germany's fears that it could lose a key ally in Europe if the U.K. quits, those hoping for a big announcement from Merkel's visit may be disappointed.
Merkel has her pro-EU integration Grand Coalition partners, her domestic audience and her relationship with France to worry about.
(Read more: Angela Merkel's unlikely government steps up)
"She will not be able to offer real concessions and the German approach to European integration remains clear," Nickel pointed out.
Germany is also pursuing closer ties with Poland, whose population Cameron offended last year by suggesting that Poles resident in the U.K. should have benefit payments axed.
Also, Cameron's concessions to the more anti-EU elements within his own party have been viewed as a sign of weakness in Germany, Nickel argued.
At the height of the Ukraine crisis last week, Germany, France and Poland sent their foreign ministers to Kiev – a move that was seen as a clearer statement of where Germany's diplomatic future lies than the Chancellor's London jaunt.
(Read more: EU imposes sanctions as Kiev burns)
- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.