If a job is to be done correctly and to a high standard it generally won't be the cheapest. The question to ask is why is the quote so low? And what qualifications do the company have? The flooring trade is not a recognised trade (yet) however there are organisations such as the NICF who test and accredit fitters making sure they are able to carry out the job to the relevant BS Standard and beyond. Before you get blinded by savings always make sure the company is able to provide you with the workmanship you desire.