Dont just relay the carpet .. think about it, why are the boards squeeking in the first place ?
Having been out to this kind of job many times, I can tell you the most likely cause. The boards are usually loose and squeeky because when the central heating was fitted the tongues and grooves were broken off the boards on the landing.
Yes it is a fairly easy job for a handyman, but you cant just go winding screws into the loose boards. The boards will need to be lifted and care taken to avoid screwing into pipework that may well be notched into the joists below the boards.
Find a local handyman and it shouldn't take half a day to make a few suports, screw down the boards and tuck the carpet in.
Having done plenty of them, I know that your £100 should more than cover it.