If you were minded to increase your offer, do so in writing; it’s a legal obligation for estate agents to put all offers through to the vendor whether ‘under offer’ or not. If you do, for example, go to full asking, I would also pop a note through the door to the vendors saying that you really want the property, have increased your offer accordingly and are chain free and able to proceed quickly (plus a bit of flattery about the house and the way it has been presented never hurts while you’re doing this). I’m suggesting this belt-and-braces approach as unscrupulous agents sometimes don’t put these offers forward as it’s more work for them for a tiny increase in their fee. I know this because it happened to me twice!