London City? Easy for private jets? Sure, if under 10 tonnes... But that doesn't influence immigration checks. You still need to get your passport checked before boarding and Border will check it on arrival.
I need to add, if the flight is operating as a commercial flight and over 10 tonnes, oh boy, it'll get the full monty security treatment. If operating as private, then much of the security pain is spared. Passport control doesn't change.