Aircraft impressed into UK wartime service: under what power?

Excellent, thank you. So the Emergency Powers (Defence) Act did indeed grant the power to authorities to requisition property. Subsequently the Compensation (Defence) Act established guidelines for compensation.

http://www.legislation.gov.uk/ukpga/Geo6/2-3/75/introduction?view=plain+extent

Clause 4:

(1)The compensation payable under this Act in respect of the requisition of any vessel, vehicle or aircraft shall be the aggregate of the following sums, that is to say,—

(a)a sum equal to the amount which might reasonably be expected to be payable by a person for the use of the vessel, vehicle or aircraft during the period of the requisition, under a charter or contract of hiring whereby he undertook to bear the cost of insuring, maintaining and running the vessel, vehicle or aircraft, and
…

continues with verbiage associated with damage and loss.

So the owner received a payment, on a monthly or longer timescale, roughly equivalent to chartering the aircraft. Seems reasonable; gave the forces the aircraft they needed in a crunch, whilst financially discouraging them from holding them indefinitely.

I understood the the aircraft impressed, or reasonable substitute, was returned at the end of the war. One Tiger Moth or Dragon Rapide was, after all, much the same as another in the big picture. Few of the individual examples will have survived, but presumably their ownership can be traced through their history?

You could start by looking at the Emergency Powers (Defence) Act 1939.

Obviously meaningful compensation was dependent on winning the war.