Great advice above - google "Tenancy Deposit Scheme" for info, and don't accept an apartment without it. All genuine landlords will be happy to be use the scheme.
The property market in London is a lot easier than in Geneva, so if you have any doubts about a landlord or apartment, don't take it, there will be plenty more.
Look on gumtree for private landlords which will avoid any agency fees.
You might find things easier using an agency though. The biggest is Foxtons:
http://www.foxtons.co.uk
But their service can often be pretty shocking! They do have a lot on their books though, and you're well protected with them.
Others are:
www.ludlowthompson.com
www.abodelondon.co.uk
If talking to an agent, ask them upfront what their fees are, so there are no shocks! And check if there are fees for extending/redoing the contract after the first year - you don't want a nasty shock a year after settling.
Wander round areas you're interested in, and you'll probably find a couple of local agencies as well.
Finally, if you don't know what areas to look in, ask! London is huge, with so many different parts, it's like lots of different towns. Everyone has different ideas about the great places to live, but I'm sure plenty of people here can warn you off the dodgy areas :)