Not quite. Anything from London Control inbound to Farnborough, Lasham, Fairoaks, Blackbushe and Dunsfold is handed off to Farnborough Radar; Odiham having their own radar handle their own traffic. Only Farnborough and Odiham presently have instrument approach procedures (Lasham had radar until recently but it was 'withdrawn' and looks unlikely to be replaced) whilst the other airfield have visual approaches only. Likewise all departures from the first 5 airfields to join the airways system are handled by Farnborough until there is no other traffic to conflict with them, then they are transferred to London Control.
The above is 'simplified' as each airfield has it's own little 'quirks' to procedures, but it gives you a basic idea of how faster traffic is able to mix it with light aircraft round the area.