Hi
We haven't had ours done but we're in the process of researching it.
Because a basement is a relatively large job I'd go for a company that can show you round other people's houses that they've done. You really want to see three or four basements that they've done. If they can't show you previous happy customers walk away!
Secondly, basements can involve a lot of work that impacts on your neighbours. At some point you might be digging almost underneath your neighbours house and their house will almost certainly show some effect. That means you need to see insurance and discuss in detail how they've handled grumpy neighbours. If they say they've never had them I'd guess they were lying. I know of one person who started digging for a basement (about three months of really heavy work) and had her neighbours incandescent with rage hammering at the front door within about two minutes. The work had started in Feb and the neighbours eldest was into the final stretch of A Level revision. Their relationship with next door has never recovered. And I mean really poisonous.
I have heard that London Basement Company (
http://www.londonbasement.co.uk/" onclick="window.open(this.href);return false;) are expensive but good. Someone I know used them, even though they could get a cheaper quote elsewhere, because she felt that the premium paid was in effect was a "keep the neighbours happy" payment. On the plus side they washed everyones car in the street when they got covered in dust. On the negative side they charged her about 2k to put boards down in her house which she thought was included. Hurlingham Developments (
http://www.hurlinghamdevelopments.co.uk/" onclick="window.open(this.href);return false;) also have a good reputation and they advertise on this site but I can't reiterate enough go you need to see stacks of happy customers, look at the work and ask those customers what extras they got hit for.
If you go ahead please share!, I think building work is one area where sharing information is so important!
Good luck.
TPTP