For our last proper move we used Cadigan Tate who were ok, they did all the packing for us (highly recommended) but left early lady one saying they had plenty of time on the second day to pack the remainder which they did which was subsequently rushed, some things were very badly packed and damaged and we were an hour late leaving the property.
For a smaller moves whilst having building work done we used Aussie Man and van twice then Kiwi Movers. The first Aussie team were great, the second slow. kiwi movers were awful - amateur, extremely slow and basically just some backpackers looking to earn a few pounds.
I would recommend the packing service, saves hours!
I used http://www.gentlemanandavan.co.uk to remove and store furniture for a week last year while having floors sanded and they were great; took good care and were able to remove, arrange storage and bring everything back.
You know, every moving company offers packing services, but even so, most would recommend that you pack the valuable china yourself. They offer insurance, but still prefer you to take the responsibility for your most precious items. Don't know why.