Sounds like they are affiliated in some way with Carcrapped if you have to take it there to be checked. If they are anything like Carcrapped in regards to it's morals then be very wary of them and any techniques to rob you of your money. Also, by taking it for checks to be done, this is their chance to kick the valuation downwards - could end up being a not-so-quick sale for not that much money.
Having said that, if you are happy with their valuation (and they adhere to it), the funds are in your account before you hand over the keys and you send the relevant bits of the V5 to the DVLA to transfer ownership, who cares if they are a reputable company?
Have you tried a private sale? If priced keenly a private sale can be quick too, you know...
JJ