Why should it cost more??? If it's done 120k modest motorway miles (which is very likely), everything inside the engine, clutch, gearbox, etc, etc. will be much less worn than on a 80k traffic light warrior.

The important bit is neither mileage nor the stamps in the service book: You simply have to find out, how the car has been used. If it belonged to some self-employed chap who used to commute between Aberdeen and Brighton once a week you've found yourself an absolute bargain. It will give you less grief than a "pampered example" from a so called car-enthusiast who only used it to drive to the shops where it never really got up to temperature.