I don't know what the process is if you go through a GP, but when my flatmate had a termination, she wasn't registered with a GP and just went directly to Marie Stopes. It cost a lot of money but she was able to have the procedure within a few days, whereas she would have had to wait weeks going through the NHS. This is just her experience though, I don't know how long it would normally take to arrange things on the NHS, but just to say there is the private option if the funds are available.
She said the people at MS were really nice, she had no complaints. From talking to women here, it sounds like abortion is treated much more matter of factly than back in the US. You can have an abortion for whatever reason, well into the second trimester. There are also a lot of counseling and support services available.
(PM me if more details on Marie Stopes would be helpful...)