Go and see them. Are they smart? Uniforms? Employed staff rather than brought in per job. Smart vans? You should get an idea how professional they are. You could ask for testimonials too. Then give them info about your move. Size of house, list out big pieces of furniture. How many boxes do you anticipate for the kitchen contents, books, toys etc. Are you moving far? Do you anticipate a weekend move? Hth.
Try and get recommendations locally - try local mumsnet for example. A firm that's been around for ever. They may come and do a visit to give you a quote. And do they do a packing service? I would starve for a month to pay for that!!
You need to ask, 1.About the company's history. How long have they been trading? 2.About the logistics of the move. What time the van will arrive? What is the estimated time to finish loading up and time of completion? 3.Do they offer insurance and at what level? What is and what is not covered? 4.Will the work be carried out by themselves and not farmed out to another company? 5.Do they have any references, can you contact past clients?
Go for a company that actually comes to see how much stuff you've got. Ensure they look in the shed/garage/loft so their quote takes the stuff in those areas into account.
Do they provide 'hanging'/wardrobe boxes? This means you (or they) just lift stuff off the hanging rail in your wardrobe and hang it in a box with a rail. Will save you packing all the stuff in your wardrobe. That said, if we ever move again I will pay for a packing service. It was a major pain and seemed to go on forever.
Ask what they'll do if they van they provides doesn't turn out to be big enough (ie. if they've underestimated the size of the van needed). This happened to us. Fortunately, they had a spare van and driver that day. If they hadn't it would have been a nightmare.