Another vote for CRGH here. I think we were seen by Dr Abramov, but also remember Dr Saab. This was 2014.
We were lucky and in the end were successful on our first round of IUI, so never needed to progress to IVF.
General memory was that appointments were sometimes fairly chaotic and often ran late (clinic is part NHS, part Private, but we weren't eligible for NHS) but that fact did make me feel as though they were more open to discussions around which tests/procedures were necessary, rather than expecting you to be happy to pay for absolutely everything under the sun. Friend who did extensive research and spoke to various doctor friends settled on CRGH as the best option too (she was also successful)
Out initial rounds of tests cost us approx £4000 for me and husband. There's a lot they need to check out before moving into IVF, so keep that in mind (thyroid, HIV, vitamin D, clamidyia etc etc. None extortionate but takes time and adds up)
Also relevant that you will be travelling there a LOT, so transport from your home/work needs to be taken into account. This may be less of an issue now as a lot of people are currently able to WFH.
Good luck!