For my sins I was once a beleaguered Thames Radar London City CTR controller. Regardless of Class D and its access rights etc, sightseeing transit flight were, quite frankly, nothing less than a nuisance. Confined precision, time-constrained commercial operations take place in that tiny CTR, and the procedures coupled with Cat B and Cat A operations over the metropolis render it intense aerial activity. I doubt that the situation has changed very much. I suggest that you do yourselves and everybody else a favour by circumnavigating this very small CTR rather than encumber the LCY operation by flying over a highly built-up congested area which has very few alight-clear options. Following the M25 makes light work of it for all parties...