It was about the size of a blackbird, but had a read stripe on top of its head, a black face and beak, a green back/wings with yellow wing tips and a light brown chest. I am in suburban London.

There are several different ways to identify it. You could get a field guide. These books have descriptions and photos or artist's renditions of birds, organized in a logical way that makes it easy to go through and identify birds that you see. Another way would be to take a photo of it, post it on a website and put a link to it here so people could see it. It is easier to identify a bird from a photo, rather than a description.

I would try to identify it for you, but I am not familiar with the birds in England.

Why not go to a source right there in your own city.

London Natural History Society
Ornithology Section: London's Birds
http://www.lnhs.org.uk/ornithology1.htm