Bear in mind, that if you bought from an online retailer, it would cost in the region of £1600 used or up to £1800 for some retailers (particularly those who have a store front as well, such as LCE or one of the local independent stores), they would usually offer something like a 3 month warranty, so you'd have some comeback if it was faulty on arrival. If you factor in the lack of a warranty, I would hope it would be a maximum of £1600, but it would be better closer to £1400 for what is essentially a private sale, so that the cost of a service can be accounted for. For a better guide, you would need to know how much a service is likely to cost, which I have never had to do.
The other thing to bear in mind, is that there is currently a lens rebate of £150, so that brings the cost of a new 70-200 MkII down to £1650-1700.