A cleaning firm would take this on.
Google cleaning companies in your area, or look them up on Yell.com
You could try franchises such as Poppies or Molly Maid but to be honest they dont do a good enough job in these instances in my experience. They are great at the domestic stuff but I see this as deeper than domestic.
What it costs depends on what you want done.
Do you want carpets / windows / skirting boards etc.
How many rooms. How many bathrooms.
I wouldn't consider getting any cleaning done until the building work is finished as dust will get everywhere and will undo the hard work.
I would think it will be between £200 and £400
I run a property management company so depending on where you are I may have contacts for you?