This is a difficult question to answer because it largely depends on what you would like to do in your free time and how expensive your tastes are.
You will need money for
- meals (other than breakfast and the group meals included as part of the trip)
- admission fees (theatre, galleries, attractions - many museums in London are free though)
- shopping (though please be aware that there are restrictions on the value of goods you can bring back to Germany)
- public transport (if you want to travel outside central London)