Other option of course is to put the pax across to an operator who has the right types to get into London City ! In fact I wonder why they don't do this themselves unless you're beyond the range.
Only large bizjet with transatlantic range cleared for LCY is the Falcon 900EX.
As for other airports (London area):
Heathrow - expensive for GA & difficult to obtain slots
Farnborough - not 24H, wrong side of the City for Canary Wharf
Luton - again, the distance to Canary Wharf but is 24H
Northolt - not 24H, can be difficult to obtain slots, active RAF base, expensive & again, on the wrong side of London
Stansted - 24H, direct Motorway links to London
Biggin Hill - not 24H but not that far from Canary Wharf
Gatwick - similar to Heathrow
the only other posibility is Southend, should be able to get a G5 in & out of there easily enough
FC