Yes, such routings can be approved subject to the traffic flow at City Airport. The contact frequency is Heathrow Radar on 125.625 and clearance will be not above 2400ft AMSL.
BUT there is a problem for single engine aircraft to comply with Rule 5 of the Rules of the Air Regulations which requires an aircraft to fly at a height which enables it to land clear of a congested area in the event of an engine failure.
The Rule is here:
The Rules of the Air Regulations 2007