Hi twounder 2 and welcome!
SJ - work out the top you are prepared to pay and offer that.
We were involved in a bidding war with 3 other people for this house. So we offered to pay asking price and we got accepted, though the house was worth more. Even after that, someone nearly gazumped us the day we were due to exchange!!! The seller tried to stall exchanging on the day, and we said "exchange by 12 noon or deal is off". We later found out he was waiting for another offer from someone who was planning to bid above us just at the point of exchange!
You need to work out what you are prepared to pay and offer that (as Ros said really). Otherwise you may kick yourself afterwards.
How much do you want it?
Well my toothypeg op went very well - the dental surgeon at the hossie is super and does keyhole surgery through a teeny hole srilled in the filling, through which he looks with a microscope!
CoV - Lodger is OK but she is very stressed atm 'cos of college pressure and DH delays in arriving. I simply asked her to tread more softly/not bang doors late at night and she got very childish and defensive. Then said "anything else?".
She was very quiet last night though, so mission accomplished