The only way to get the best, fixed prices from contractors is through a managed 'competitive tender'. It sounds complicated, but really it is just a formalised way of having several contractors price the job and submit fixed prices by a given date. As it is 'competitive', the contractors will need to provide best prices in order to beat others and win the job (although the lowest price is not necessarily the best option!).
There are many options out there, ranging from small 2-man bands through to larger contracting companies with offices and a chain-of-command. Clearly it is not fair to have very small companies tendering against larger contractors as they will have completely different setups and overheads. Often (but not always), smaller companies can be less organised and slower but at the same time considerably less expensive. Larger companies are more likely to be better organised and complete the work on time, but you will likely pay a little more for this.
You should think carefully about what is important for you, meet any contractors you intend to ask to quote and ask them to show you round their previous work if possible.
Once we have a shortlist of 3 or 4 Contractors, I will send them the tender package and talk it through with them to ensure they will submit a quote on time. Contractors will be given 3 or 4 weeks to price the work and will visit you early on to introduce themselves and see the property in question. Once they return the quotations to me, I will analyse these and clarify any issues with them before compiling the figures and sending to you as a succinct document. We can then discuss the options and decide which contractor you would like to appoint.