Hi!
I can see nothing wrong with the way you handled your communications. We teach students to use "WILCO" only to acknowledge requests by ATC to report something, but according to the ICAO Doc. 9432 Radiotelephony Manual, "WILCO" should also be a valid answer to a request to remain clear of controlled airspace.
But then, maybe, the UK has it's own special rules as usual?
Happy landings, max