It's really not that bad but can you get more for your money somewhere that isn't a new build?
The main living room in our London flat is 4m x 5.3m. We have used it as a sitting room with a formal dining area in the past with an 8 seater table and sideboard in 1/3rd of the space and 2 x 3 seater sofas, a coffee table, console and large bookcase in the other 2/3rd. That is not very different from the living space you have minus the kitchen.
It feels a lot more spacious than the average London flat living room, although it has high ceilings and windows on the long side, which makes a difference. I've no doubt a modern developer would squeeze a kitchen into the space nowadays too based on the more recent conversions I've seen...
I think what makes the long open plan living spaces in new build developments look like a corridor is that they usually have the windows on the short side so the focal point (window) is a long way away and the room can be dark at the opposite end. You can counteract that with clever interior design tricks (eg mirrors, alternative focal points in the different zones, not placing all the furniture against the wall).
TBH, it was never our family home with DC and I think it would have felt a bit cramped with a gazillion toddler toys and a Brio railway in the middle of the floor but no worse than your average Victorian terrace.
I am going to go back on what I said before about bedroom 3 not being suitable as a sitting room. I think I would buy an L shape sofa and chaise that is a sofa bed for that room and use it as a multiuse second living area/guest room/playroom or study. You don't actually need easy access to the balcony from bedroom 3 and it would look fine with a chaise in front of the balcony french doors. If you have another DC, I would even consider having them share a bedroom for sleeping and use bedroom 3 as play space, especially as bedroom 3 isn't really suitable for a child (too noisy at night next to the living area and it's better not to have balcony access from a young child's room).
The problem with new builds is they want to squeeze in as many double bedrooms as they can so all the bedrooms are suitable for adult flat sharers to be able to sell to landlords whereas slightly smaller bedrooms and more living space would be a better layout for families.