I suggest you get at least 2 quotes and better 3!! Also, make sure they are from fully qualified electricians and not part trained DI's, registration with NICEIC, ELSCA or any other of the scheme providers will not guarantee the operative is a fully trained electrician unfortunately. When you spend £4000+ on a complete rewire, you expect to increase or maintain the value of your property, so forget any notion about a mini trunking installation it will do neither!! lol!!
As a landlord, this is not the time to scrimp and save, ...get the job done once and right by a professional. The installation will then last and more importantly, be safe for any future occupants!! ...And probably will see you pushing up daisy's before it needs re-wiring again!! lol!!