Hi and welcome to WB. It's a bit slow on here nowadays as FB has taken over.
Regarding Green Laning; your best bet is to join the TRF, (Trail Riders Fellowship) Although a national group, there is a Wiltshire group who meet for a social monthly at The Pilot in Melksham. They do lots of runs each month catering for beginners through to experts, gentle to challenging routes, including many routes using the plain. Much of the plain can be out of bounds at any given time due to MOD exercises when the red flags are up and you can get your bike confiscated if you are in the wrong place. You probably already know, your bike has to be street legal to ride on the plain and byways.
https://www.facebook.com/wiltshiretrf
