OP I think you should just go for it with that offer- it's almost 80% of asking price.
I think all this worry about "cheeky offers" and "offending the vendors" is just ridiculous!
Property prices are ridiculous at the moment (we're in SE London)- the flip side is, do sellers or agents ever feel embarrassed about the crazy prices they are asking for? no, I don't think so, at all.
If it has been on the market for a year, I'd say the owner would be grateful for even an offer and bite your hand off.
However, if they are just hanging out for that one asking price, they might be waiting a long, long time...but they may be ok with that.
Part of the bigger problem IMO is estate agents earning a % commission.
They should really earn just a flat fee e.g. they get their £2k "earnings" whatever the property is sold for, so their motivation if you like, is to just get the property sold rather than haggling over 10k here and there.
This is all coming from a FTB looking in SE London.
Owners have made at least 100k on their homes, if not much much more.
The market has slowed down but I don't think sellers & agents want to really acknowledge this.
If FTB stop buying/are unable to secure appropriate mortgages, then the whole property game tends to grind to a halt.
We will most certainly be going in with an offer of around 80/85% of asking price (when we find somewhere suitable)...part of it will be avoiding emotional attachment or worry that we will lose the place.
There is so much on the market at the moment (2/3 bedroom flats) that there is always something else to look at.
Good luck OP! Let us know how it goes 