As long as it's not more than 50% of the width of the original house, not more than 3m high at the eaves, and not more than 4m high at the highest point, it would be p.d.
They would probably not accept the application if they were satisfied it was permitted development.
If they made a mistake and treated it as a normal planning application, then (1) if it was approved, that would be OK for you or (2) if they refused it, it wouldn't matter because you could still build it under p.d. (as long as you are sure it would fall within the rules).
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