Assuming you're looking at a like for like swap - i.e. both sets fit each other and no further adjustment or trimming is necessary (maybe the old ferrule or two) - you're either looking at a per club cost (16 irons in total?) or a basic cost to do the job lot per labour rates. I'd guess something around the £150 mark - your best bet is to phone your proshop and ask.
You could do it yourself very easily.
As long as the shafts match as nemicu says and they are steel it really is simple.
I have no idea how much a pro would want but £150 seems excessive IMO.
If you are not comfortable to do yourself take the above advice and call a few up - you can then decide from there.