A lot of 'local' firms are subsidiaries of national firms.
We moved with Britannia a few years ago, and it was £1000+ for a 2-bed flat but that was quite a distance. We had three companies do us quotes - they came round and did detailed assessments. We knocked them down a lot though, so do try and barter a bit.
We've also moved with man and van type outfits without too many problems. We packed then.
We've moved twice in the last few months with Curtis/Whites (same company). We had one fab move, and one terrible move. The second one we had an agency bloke (paid by the move, not the hour, so worked v.quickly), and a Polish bloke (no English, no training). We had a lot of damage. This was from a really reputable company. So you don't necc. get what you pay for. We didn't take their insurance as our home insurance covers us for moving (check yours though, most don't), so we had to claim off of our home insurance, and then they claimed it back from the removals co. as they admitted liability. Nightmare.
Think distance of move plays quite a large part in things.
If you have to move on a Friday, consider asking if they'd reduce the price to collect Thursday and deliver Tuesday if that is an option for you. We often do pack/load Thu/Fri and deliver Mon/Tue. We enjoy the break from it all over the weekend.
Hope that helps