More than likely it will probably require planning permission.
That simple sentence could lead to a process that might become a lot of trouble or else be plain sailing.
AFAICR, only houses that were originally in one ownership and then sub-divided can be put back into one ownership can be considered exempted development.
That doesn't seem to apply in your case.
As long as it doesn't contravene some obscure provision in a development plan the issue of joining per se should be a formality since there is no nett additional development occurring - it just needs permission.
Bedspaces, parking spaces, open space are all as catered for in the development plan.
However, the real issue with planning may well be the look of the house as you attempt to generate a convincing and useful entrance.
Not much of a problem if the entrances are together on the party wall, it becomes a different kettle of fish of they are on opposite sides of the semi-detached pair.
While the entrance is easier if the existing ones are side by side, the potential to create really big rooms is better if the entrances are at either end.
The trouble with making "two into one" big rooms is that they can make the ceiling look too low it if it a normal ceiling height to begin with.
There are pros and cons depending on the location of the front door, but that's for discussions with your architect on foot of a developed brief.
Then you need a meeting with the planning officer for the area to see if it will fly.
You may need a survey done and a full set of planning drawings before the planner will hold a Section 247 meeting with you.
Long before you get there you could just ring him/her up and ask fro comment on your proposal.
FWIW
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.
