As for LCY - don't get me started. Not only are they not keen on overhead transits, try asking to land there in a single You'd think you had suggested treason.
I've landed at LCY 3 times in a single
As for LGW, I still believe it's easier to say "no" than "yes" these days.. It was commonplace in ye good old days. Nothing has changed, the runway is still in the same place, maybe a bit busier, but even in a permit to fly aircraft with a handheld, I was never, ever refused a transit Redhill to Shoreham. In the 10 yrs I have worked there, I've only ever seen one single overhead and that was taking photographs... S/E helicopters on the other hand...
Progress!
