Six Keys - based in Acton and a few other places around London.
They were recommended to me by a few friends, and made our moving day almost pleasurable.
Was £950 for moving a jam-packed 2-bed 1st/2nd floor maisonette with full loft, to a house 40 min drive away. They supplied boxes but we packed, and they checked up on us a couple times before the move to ensure we had enough right-sized boxes and were getting on with it.
Five chaps at one end, four at the other, arrived 8am, worked until 7.30pm putting everything in the right place.
Even moved the fish tank, and nothing broken at all.
They also kept our moving date open despite our exchange date being postponed for two months, and kept us abreast of alternative dates in case we had to delay further (we exchanged on the last day they could hold the date for!)