We used Bishop's Move in Oct-08 and used their complete packing service - it came to just under £1,000 but was worth every penny. Three men took almost three days to pack our 3-bedroom (& one v. full loft) house (into two huge lorries - how did we get some much in,) starting at 8am & finishing at 5-ish. I hate to think how long it would have taken my husband & I considering we had a 3-year old who would have spent most of the time 'helping' by unpacking as we packed. Plus they bring their own boxes, packing materials, etc so that's included in the quote. We only had 2 breakages (a plate & a glass table top) from that & with photographic evidence they paid up for the items with no problems.
Things to note - check your home insurance - you probably don't need to take out for extra removals insurance (as 'offered' by most companies) so long as you get the removals company to pack your 'breakables' (you can do the rest) since the move will be covered by your home insurance (plus up to 7 days in storage).
Some companies will bring down & pack your loft for you so long as you have a fixed ladder, boarded loft & lighting.
Remember the packers do this for a living - they are probably a lot quicker & better at it than you.
They will pack EVERYTHING - empty bins, put your over night bag, your child's precious toy & any paperwork you need for your move in your car & lock it before they arrive or it could end up in the van before you know it! They packed our DD's Catty Cat Cat, which had to be unpacked and my husband's newspaper for the day!
When they arrive at the other end, they won't unpack but they will assemble large items of furniture for you such as beds & wardrobes. Write / print off labels for your room (eg 'Bedroom 1', 'Dining Room', 'Living Room', etc) and stick to the doors with blue tack as one empty room looks very much like another. That way you can tell them 'Bedroom 1' for that box without having to stand on the landing & pointing all time, meaning you can get on.
Good luck.