40-50 guests & a budget of £5k in London. Is this possible?

I would suggest that you look into hiring local community centres and getting a mobile caterer. Either that, or finding a restaurant that seats around that number. Both these options are likely to be cheaper than booking a regular 'wedding venue'.

Also, think about what you really, really want to have at your wedding, and don't be afraid to ditch anything that isn't super-important to you. Make a budget - start off with the most important things and their costs/approximate costs and gradually work down towards the 'would like to have but only if we can afford it' things. If you run out of money before the end, just don't have the stuff at the bottom of the list!