http://www.direct.gov.uk/en/HomeAnd...eetcleaninglitterandillegaldumping/DG_4018684
So apparently there is no "Law" but other systems in place. I guess it also depends how big a fire you are going to light, a catering sized tin with a few twigs in can't really be called a bonfire, and is quickly and easily extinguished once lit.
Wings
As you quoted there are no direct laws against the lighting of bonfires. I looked into this when I was doing my Countryside Management course ('cos I wanted to light some large bonfires ).
I can't remember all the details now but basically you can get away with it if there aren't any complaints. You just have to use common sense about how big your fire is, which way the wind is blowing and who is likely to complain and why. If it's just some snooty neighbour who isn't really being inconvenienced and it's only an occasional fire then the police or environment agency will probably just let it go.
However there are some laws about smoke blowing onto roads that you need to be aware of.