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They don't look at the value, they look at the purchase price, most of the time.
The times when they don't are when you are buying from family as a family gifted deposit purchase or when buying from landlord or council right to buy.
Commercial properties or renovations and self builds have slightly different rules, for mainstream residential, most lenders will go by the above rules.
If you are buying under value and not getting a gifted deposit, then Getting the property cheaper doesn't matter, though some lenders will refuse if they decide that it is a 'distressed' sale.
Acliff-
They look at the value and the purchase price. You need to declare if you are paying below mkt value and explain the reason (unless you are doing fraud), but then the ltv should be based on resale value not transaction price.
For this kind of purchase a broker should be used as the purchase will not fit the profile of a standard retail mortgage.
Ramsaye
Someone I work with did this. Banks look at the value (£300k) vs the loan (£200k). Not the purchase price.