Well, would you want competitors to see proof of your offer? Or would you consider that privileged, sensitive and private? It’s an odd question to ask. It highlights your uncertainty and lack of experience.
The loft room is not liveable space and the big one is included on the square footage calculations. There is no clear floor plan showing layout so I assumed all loft rooms were accessed via ladder.
However, something is stopping this loft room being recognised as living space - without viewing it I don’t know what that is but my potential issues would be: did they switch out the joists when turning it into a room? Usually lofts have smaller joists and these are changed to accommodate constant use. Is there a hallway for fire safety? Are the stairs steep/narrow/head height issue? Because ordinarily additional staircase would eat into the floor space below. I would not be happy to use the loft room due to safety concerns.
However, someone savvy might sit on this. Wait for the surveyor to flag it. Come back with a much reduced offer and point out your cash status means you don’t have to run this unofficial living space by a mortgage provider - who might well want it officialised.
But when a room like this has been “done up” the temptation is to use it. For me that would rule it out as it is very unlikely to be sufficiently safe.
Someone flagged radiator, letterbox. The radiators are old and probably don’t meet btu requirements. It wouldn’t be hard or expensive to just switch them out and correct the piping. Dependent on how it’s done 1-2 days 600 quid plus parts. Not something to stop you buying a flat and with the same perspective I’d expect to replace that boiler soon too. But these are trivial costs.
Biggest expense would be the new kitchen.
Do you not value a garden?
Bottom line: is it bad value? No not really (lease and ground rent terms dependent). Are there better properties at 390k in East London? Yes, in my opinion there are.