There is nothing, in theory, to stop a traveller or in fact anyone claiming the land if it is not registered to anyone then all they have to do is prove they have used it for 10 years and it can be officially registered in that said persons name. If they have no access to the land then they obviously cant claim that they have used it. If the land is at the end of your garden then you could effectively use it and go on to claim it as your own if no-one objects within that time.
If I were you I would use the land, if the council does indeed own it, you'll hear from them soon enough. The most likely way for them to find out is a jealous neighbour who sees you expanding your boundary when they cant or wont do the same.
Search google for 'how to claim unregistered land' - in amoung all the spam websites there is some quality information that will explain how to go about finding who has the title to the land and if there is no-one, how to go about claiming use of it, eventually claiming ownership.
Back to the predicament though, it does seem strange that the council will not let you use the wasteland to grow your own veg and commit to a greener living in this day and age, you would think that they would maybe open the area to a number of people for a peppercorn rent perhaps then get an article in the paper saying how the local council has helped local people commit to a greener living by helping them with the supply of space to do it in. I know the job of the council should not be to spin media to a positive, but they miss out on so many opertunities to both help themselves and also help the tax paying citizens that employ them.
Ta
Baz