I think, even if you had enough ground to qualify for the Basic Payment, you would have to buy entitlements. Guess what, they sell for not much less than the income they are guaranteed to bring...
However, do check, because it has all changed a bit since the SFP was replaced by the BP.
There's no such thing as a free lunch, and any of these schemes come with significant restrictions on what you can do. Quite likely, if you were able to register your woodland (woodland wasn't eligible for SFP, as far as I understand it all, but I'm not sure about BP), there'd be some rule stopped you running pigs in there, if you wanted your payment...
Grants usually require you to do things in certain ways, which are more expensive than how you might have gone about it without a grant, and generally only give you 50% back, or less. So in general, we've found them superb for helping you get a better outcome for the money you were going to invest anyway, but they are not free money.
As to Brexit... at one point, the government said they'd keep agricultural subsidies the same for a couple of years, so if that means two years after we actually leave, and we press Article 50 in March 2017, then there are a bit less than four and a half years left. Iff the government stick to that 'promise', of course...
With such a small acreage, I doubt very much if you'd find it worth your while. But do check - the local agri accounting company should be able to tell you in a 5 minute phone call whether it's worth investigating further.