> So calling up Heathrow Tower and 'Requesting route North to South, through your overhead at 1200ft', might work eh?
No problem, done it. But you do need to be in a helicopter. (And you phrase the request slightly differently, but that's a detail).
In a small plane, I've been SVFR but only on the outer fringes of what was then Class A, now Class D. You can't get anywhere close to either the airport or central London.
When I did my London helicopter tour in April, we called "Heathrow Special", not "Radar". And yes, we did get to talk to Heathrow Tower.