We live in SW london. I'm not sure if there are any local clinics but in central London there are quite a few. We used the Bridge Centre at London Bridge and got a BFP first time we did icsi. ( I assume you're talking private?)
It was no problem at all getting there for appointments. I took the northern line straight up to London Bridge. We were never kept waiting for an appointments / scans etc. I got early appoinments and went staight to work after - it was fine. It's more important that you find a good clinic even if you have to travel a bit
We live in Watford Herts and are having private treatment in Guys, London Bridge. DH and I do shift work. To be honest, the doctor we are using is Mr Khalef and we have been lucky that we can make appointments at almost anytime, our first consultation was at 6.45pm!! We were driving into wat junct, then a train to Euston and a tube to London Bridge, nearly 2 hours each way, but now we've managed to cut our travel down to about 1 and half hours by parking in Collindale and getting one tube now. Mr Khalef was recommended, I'm going for EC tomorrow for our first ICSI so can't give you a happy ending story YET!!!! All in all it's going to be worth it no matter where you go and think of all that extra quality time you can spend with your DH
Good luck no matter where you go.
G x x