yes they are very edible..no licence is needed to hunt duck (which are on the game list)...teal,mallard,wigeon etc) but there is a season in which you can take then. look on the www.basc.co.uk web site for all info.
I don't quite see what the point of a closed season would be if people could make money letting you shoot on their land out of season by just giving you permission.
There's an exception in section 3 of the Wildlife and Countryside Act which might explain what you've heard if it had been misunderstood. But it's about "Areas of special protection" and restrictions over and above the normal closed season. See for example http://www.jncc.gov.uk/page-3614 There are also exceptions for deer, basically for farmers and other landowners to prevent the deer doing too much damage to crops etc., but it isn't just a matter of ownership. Of course things might be different if your grandmother happens to be the Queen.
Anyway, I think this discussion might be better taken to one of the shooters' sites. Although you won't find much meat on a willow tit, pretty well any bird is edible so the bushcraft aspects have been fairly well covered.