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I can only echo this having done similar a couple of years ago.
In short here's what I learned:
It will take twice as long and potentially twice as much as you think.
To mitigate the above if the builders will do it get quotes for labour only. You will want to choose your own materials for most of the finish I'm guessing. You will be quoted for what the builders can supply as standard. This was hard to disentangle for me.
Pay that 15k for the project management. Mine was a bit less on a similar costed project. I think I saved this easily on the whole cost and more importantly the stress
This was for a full renovation of a 3 story Victorian terrace (not on London) including side return extension. It was just over 240k.
I was also in the position to live with family for the duration (12 - 14 months)
I'm fairly sure this is a cashflow discussion.
Either you have the money now + the time the work takes to complete + longing out a bit of snagging.
or
Save until you do have the above or can borrow.
Or
Part the work out in bits over a longer period of time, accept that certain elements will be less than your ideal for periods of time and that the overall cost efficiency will be poorer.
Also if you're being quoted 240k this will be 300+ by the time all is said and done. If it's stressing you now then seeing the invoices roll in and your bank account run dry won't improve things. Especially if you're onsite (or what we did, live in the PiL's spare room with a 1yr old 2 hours from London and commuting 4 x per week). I can look back now and love our place. But even having a turnkey builder/architect and having most of the money in hand, it was still a lot.