I don't get that. TC is Class A, most of which is the LTMA. One cannot get a transit of the LTMA.
The Class D bits in the UK are totally organisationally disconnected from TC, AIUI. The only time there is any connection is when a flight arrives from say FL150, passes (almost inevitably in the UK) through Class A, and going into say Bournemouth in which case TC will hand it over to Bournemouth, with the flight remaining in CAS the whole time.
Flight plans are not copied to any Class D units enroute, either.