Personally I would send back this note:
"Thanks, we have already made an offer. Feel free to come back to us if you have a counter-offer in the future. For now we are persuing other properties.
Note that the situation suggested by the agent/seller is unbelievably bad on your end (and for the other buyer).
They are under no obligation, whatsoever
They are giving out zero information
It is simply a fishing trip by them.
Be aware that, as soon as both of you put in a "final" offer, let's say 110 and 115. The agent will simply write back to you saying:
Thanks for your offer of 115. At this time 120 could secure the property.
You would be taking part in a borderline scam!
Be aware that "final offer" means nothing, and gives no advantage to you!.
They will simply look at these new offers and then think, "oh these are interesting, I wonder what we can get".
There is no benefit, whatsoever, to you (or the other buyer).
Property negotiations in the UK are gritty; you have to be pretty aggressive / clear thinking.
Important! What does the phrase 'final offer' mean?
In negotiations you often use phrases in English such as
- "It's my best offer!"
- "I swear this is my limit!"
- "I can't go any higher than X!"
- "This would have to be our final offer!"
- "This is a whole-budget offer!"
- "This is a walk-away offer."
All of this is just colorful language. When you say something like "best!", "final!", "highest!" etc, there is no specific meaning.
(There is, utterly no actual legal or accounting meaning. But there is not even any "meaning" in language - it's simply "colorful language".)
Some folks have commented that the Seller may or may not be "honest". Fortunately (so to speak), that is not the issue...
When the Seller says "Send in your final offer!" it's just colorful language meaning:
There is no meaning if you add adjectives such as final, last, best, most powerful, decisive, aggressive, high, etc.
- It could be that people not familiar w/ the UK market are thinking of an actual legal mechanisms, perhaps an "auction" or "dutch Auction", "sealed Auction", "tender" or whatever.
This has no connection to any of that.
When the agent happened to say send in more 'final' offers, it is just colorful language, it has no meaning, mechanism, effect - it means literally nothing. It's just like saying enthusiastically "Send in more offers - really good ones! Let's do it!"
That "deadline" thing...
"Further to this the estate agent gave a deadline of approximately 24 hours..."
Just ignore anything an agent says about "deadlines". Do what you want in your own time.
Certainly, at any split second you can lose out on buying a house, for numerous reasons. That works both ways. Any "deadlines" mentioned by anyone are fatuous.