I used a fantastic company but they are based in the north west of England. Cost about £4000. I only came over 3 months ago.
It depends where you live in UK. We moved to the Civray area five years ago from Dorset. We found the 'big name' removal companies very expensive, so we opted for a local firm. They were not members of the trade association, but came with references and had been used by some personalities including a well known football manager. They were half the price and gave a first class service. Nothing lost and nothing broken!
Look for shipping consolidators.
You pay a small fee and then they put your requirements out to about thirty of their contacts. This gives you a better chance of finding someone who will meet your needs at a reasonable price.