Hi OP
Offer whatever you feel that the property is worth- if that's 90% of asking price, then go with it and be prepared to increase your offer.
It's difficult, but try not to be lead by your heart too much- estate agents will pounce on that and say anything to get you to increase your offer.
It will also depend on how many other prospective buyers are around (according to the EA)- if you are the only one offering then it's more straightforward.
EA's love a good bidding war. Stay firm with what you are prepared to pay- I know it's hard though when you've got everything planned out, with furniture, BBQs etc!
We are in SE London and the market is funny round here, still lots of things on from last summer- or actually, they've now come back on the market after being withdrawn after several months.
We were in the process of buying last month- had paid out for the mortgage valuation and survey, this got done and the vendor then decided they were going with another buyer 
Got "invited" to increase our offer by over 10k
I politely declined (should have just told the vendor to FO) and we moved on.
It wasn't possible as we'd maxed out on the mortgage and our deposit/savings would not have gone any further.
Think it helps that we weren't in love with the property- it was a sensible option for now as it means we get to escape from the rental trap.
Most of the properties we have seen and offered on, we've just about liked but certainly not loved! I think that certainly helps with just moving on to something else.
Good luck