Make offers that you consider fair, and walk away. If one of the sellers needs to sell then they may accept a lower price than their ideal. Be aware that the sole aim of the estate agent is not to help you buy a house, it is to SELL his clients property to the highest offer. In Scotland the rules are different. A normal case involves a property being put up for sealed bids, to be made by a due date, all of which are binding.
Buyers make suitable survey and mortgage arrangements and make a bid on that basis.
The seller then chooses a suitable bid and the deal is binding. Most lenders like borrowers who have good steady incomes and good steady jobs. For the purposes of a mortgage the purchase price IS the value. If you pay 35,000 you cannot argue that it is really worth 40,000 in order to get a bigger mortgage. If the price is dropped to 35,000 you will need a 1750 deposit.