+ 1 what RKQ has said.
You should not approach any building project on a piecemeal costing basis.
This is nearly 18 square metres in area and is not a porch [2sqm max], an attic conversion nor an extension wholly to the rear of the property.
You therefore need planning permission and you should also try to discover the lines of services in the ground - sometimes a gap is there for a reason.
Also, where did you get the idea that only two walls are required - were you intending the bedroom to be triangular?
If you are infilling between your house and a boundary wall, the boundary will need to be weatherproofed and upgraded to resist ground moisture.
If you are infilling between yours and another semi detached house, this may change its and/or your status to terraced - this could devalue both houses.
You also appear to have failed to consider the cost of drilling and fixing bolts to the existing foundation to help prevent settlement.
My best advice is for you to appoint a competent building professional with PI Cover for the planning permission and the technical drawings.
Employ a competent main contractor and registered subbies with all insurances for the building work and get certs from them all.
You may also be liable to pay Council levies as part of any permission granted.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matters at hand.