In my experience the mortgage company will happily lend the relevant percentage to the borrower, but only up to the agreed valuation, not the agreed sale price.
E.g.
Property agreed sale price = £500,000
Property survey valuation = £450,000
Buyer needs 80% mortgage.
Lender will provide 80% of £450,000 = £360,000, buyer has to find the rest £500,000 - £360,000 = £140,000
If the lender had agreed with the survey valuation, they would provide 80% of £500,000 = £400,000, leaving the buyer with £100,000 contribution.
The difference of £40,000 is a huge amount for a buyer in this scenario to make up the shortfall for, hence why negotiations with the vendor are suggested.