Until or unless the obstacles on departure from runway 20 are remediated, pretty much any airline operating at Southampton whether with ATR72, A319 or Embraer 145 will continue to see limitations. You run into these with a low QNH or high OAT, so in poor weather or on a warm sunny day, it reduces the available payload. The limitations have improved quite a bit with the recent opening of the starter strip as the declared distances have improved, but they have not gone away. What you can do/fly from that runway has changed, but it is not limitless by any means - A319/320 being better than 737-800 unless the -800 has the uprated engines (which are expensive).
That's before you get to any consideration of the operating hour restrictions in relation to a potential base by whomever.