Hi welcome to the forum,
Hope you don't mind me saying, but this has to be the oddest first post I have seen in a long time! Love the description of "leaf plants"
I know that this is the plant ID area, but if you joined so as to post this, you probably would have been better off joining a gardening forum. I am not a gardener, and although your picture looks familiar its not clear enough for me to really tell what it looks like. You would do better taking a still picture that can be posted at large scale and using something like Photobucket to get it onto the forum.
Anyway back to the plant.
I did a search on Google just entering "uk weeds pictures identification"
https://www.google.co.uk/webhp?sour...2&ie=UTF-8#q=uk weeds pictures identification
Then looked at the first four or five suggested sites.
This one is good:
http://www.gardenwithoutdoors.org.uk/weed_guide
This has close-ups of leaves
http://www.downgardenservices.org.uk/weedlf_clumps.htm
Looks like they could be violets, but I could not say for sure. My first thought had been ground ivy, but they don't look right for that. It would have been handy to know if they look like that right now, or if the picture was taken at another time, if you have seen flowers on them, or why you need to know. As I said, I am not a gardener, I just maintain my garden, and am more than happy to pour glyphosphate or boiling water on plants growing where I don't want them, without ever worrying about what they are called or why they like growing there.
Best of luck