The airport in Geneva has a unique system. Once you've landed, you're taken into a small, round building out on the tarmac to go through passport control. Then they shuttle you to the main terminal by bus. Not sure if that's how it works for all flights into Geneva but that's what we have always done at this airport including last summer when we arrived.
I would schedule at least 45 minutes (at best) to go through this process and get out of the airport. The airport is not very large.
If your bags are checked through to London then maybe you won't have to worry about them? That would certainly save you some time. Otherwise, I'm not sure how long it might take to gather your bags and get them checked into left luggage, which I'm not even sure they have at this airport...I'll leave that to someone else who knows better than I do since I've always just connected or stayed in the area. Keep in mind that if you leave the airport, you'll have to go through the process in reverse going through security, etc., which could take some time.
The airport in Geneva is just north of the main part of town and it doesn't take long to get there. If you are able to catch a taxi from the airport you'll be at the lakefront in less than 20 minutes if the traffic isn't bad. Keep in mind that rush hour in Geneva and around the north side of the lake is as bad as any I've seen anywhere...depending on the day of the week you will be there, this could be an issue.
If I just had two hours I'd have a taxi driver take me down to the lakefront so I could see the Jet d'Eau and then to the old city around the cathedral, taking some time to walk around. It's quite lovely with winding, cobbled streets, and there are some really high quality antiquarian bookstores and dealers in all manner of antiques and art. The cathedral is worth a look as well and has a fascinating excavation underneath that goes back to the 1st century. Well worth a visit. Great little cafes and restaurants as well.
If you had 6.5 hours then I'd say to just go for it. 5.5 is pushing it but you will probably be OK??? Your call of course...