It can vary enormously, depending upon the make and model.
To get a rough figure, find out what the part costs from here:
http://www.laptopscreenonline.com/laptop-screens-35-w.asp
PC World charge the cost of the screen (but be prepared to pay significantly more for it from PC World than the prices quoted in my link) plus £50.
A local PC repair shop would probably get the part from somewhere like my link (possibly adding perhaps 10% to 20% onto the price as their profit for supplying it to you) and then charge you perhaps £40 or £50 for the labour.
Wherever you go, make sure that you get a fixed quote (rather than an 'estimate') before agreeing to anything. There are plenty of places that will happily charge you three or four times a fair price.