This is my understand of how it works in the UK:
Any airport that is contained within controlled airspace (e.g. Southampton, Bournemouth, etc.), you depart IFR in the way you're used to.
For any airport outside controlled airspace, file your flight plan on the ground, and depart IFR while initially cruising low outside controlled airspace, so maintain your own avoidance from terrain and keep a good lookout if you can:
- Towered: Your tower/departure unit should be able to co-ordinate your clearance with the en-route facility.
- Non-Towered: After leaving the AFIS/AG frequency, contact your nearby LARS unit or London Information when outside LARS coverage, and they can co-ordinate your clearance with the en-route facility.
Once the clearance is given, expect to climb much higher and it should be easy from there onwards.
As Southampton airport requires mandatory handling, contact Signature Flight Support for more information.