As an estate worker, we very rarely have fires in woodland. The reason being that fires can damage the soil as well as the roots of trees of course; and it's surprising how long the damage lasts for. I always grimace when I see a programme on TV where they do have fires in woods. All the old (and retired) woodsman (hurdlemakers, coppicers, so on) I know would have a fit if they saw a fire in a wood.
However, small fires, properly located, shouldn't be much of a problem (along with permission and common sense as mentioned in the other posts).
I don't think there is any specific national legislation that forbids fires in woodland (it's usually found as a subsection in Parliamentary Acts such as the Wildlife and Countryside Act and the CRoW Act) but there are local byelaws in place. Suffice to say that any protected areas, nature reserves, SSSI's, etc. have full protection from camp fires, barbeques, and so on.
Scrubbity