When I was a controller on Farnborough LARS East in 2008 I always suggested that people crossing to Le Touquet/Calais remain on my frequency for FIS (called 'Basic Service' at the moment but likely to change) and alerting service so that I could keep them identified on radar as far as at least the FIR boundary both from LYD and also from SFD, that way if anything happened, I could provide an immediate alerting service via D & D which was just one button push away and was always answered immediately .
OK it was outside my area of operation but I had excellent radar coverage (as low as 400ft amsl over Pevensey Bay) and my opinion, safety overrides all else so I had no compunction in 'bending' the rules.
I don't think this happens nowadays as I retired in late 2008 and as far as I'm aware the controllers who followed after me weren't willing to provide this service however you could always try asking Farnborough for Alerting Service on 123.225..