This is a difficult issue. I am clearly extremly fortunate in that all my shooting is free, be it rabbits/pigeons, vermin, foxs and deer.
Its come through being close friends to landowners and approaching others in the correct manner.
I have come into deer stalking up the ladder so to speak, .22lr for rabbits, then c/F for foxes and then because there is deer on the ground stalking. I supose through this process i have built up considerable experience, knowledge and contacts which have resulted in my current situation.
If you havent got this behind you it must be extremly difficult to get on the ladder.
It is often a game of chance and luck. 20 yrs ago I moved frowm Shropshire to Avon and left thousands of acres of shooting. I was lost, yet one day I called into a local farmer and asked if he owned a field of barley which was being hammered by pigeon. He said no, cause it was not his field, but i was welcome to shoot the pigeon on the wheat behind his farm. Next day I shot 50. He was pleased and inquired what else i shot, I told him and hey presto cart blanc to shoot on his farm. Its now its more of a case of a phone call from him saying he has got some more ground and can i sor out the rabbits/foxs.
Never looked back.
The problem is getting your first lucky break.
It does help if you keep your eyes open. Daily I drive from Bristol to Taunton and I see roe almost daily. The same ones are in the same area and clearly they are not being stalked (or there are a hell of a lot) so if i was inclined I suss out the ground, google it, find out the owners and then make some enquiries. You only need to get one yes.
Clearly Hampshire might be a bit more difficult but you just got to push on doors and one will open.
Good luck, if you perserve it will happen.
D