P.S. On second thoughts, they might not allow you to transit the Class D as high as 2,500ft as you'll likely have airliners approaching Heathrow inside the Class D at 2,000ft or so if they're on the ILS..
Indeed the clearance in the London City class D is likely to be "not above 2000 ft". (I make no comment on the legality or otherwise of doing this in a single).