My advice would be 'don't be in a hurry.' Expect to look at a lot of cars, and then decide what you want: 230, 250, 280; auto or manual; is colour important (or are you prepared to respray the right car (£££ for a good job); do you want a car with a hard top; are you prepared to fix some rust, etc, etc. Once you've seen a few you'll develop a view of what you like.
There are a few sellers in London and I've never seen one of them have a car for sale that hasn't got obvious problems or which went on to develop problems later. (ie was 'well prepared')
Join the MB club and ask around. There are a surprisingly large number of 113's in the UK club, so go to a few meets and get to know people.
Personally, I'd be more inclined to go down the private purchase route than buy from any dealers that I know of in the UK. There are some good cars out there in the hands of club members.
An alternative to consider (if you don't mind a LHD) is to import from the US where you will get much more for your money.
To give you an idea of what I sense you may be looking for, check out
www.motoringinvestments.com
