Can anyone help identifying a plant?

Hi - I have noticed a plant which appears to be growing 'wild' all over the place where I live (Lincolnshire) - along the bottom of people's walls, sometimes through the cracks in the walls, and along the small gaps where the pavement meets people's gardens.  It occupies a similar environment as the valerian which grows wild everywhere. It has grey-green foliage and a profusion of small white flowers which have come out in the last week or two.  Some of the clumps have grown really quite large, perhaps a couple of foot across, but it is never more than around 10cm tall.  I am hoping to find out its name so I can plant some in my own garden. any help much appreciated

Could be cerastium tomentosum (snow in summer)...? Needs a sunny, well-drained position. And you'd better be sure you really want it, lunarz, cos you'll never ever get rid of it once it gets hold! I love it myself mind you... 

 Thanks Auntie Betty - here is a pic - does that look right?  I don't kind if it is a bit of the thug, as it looks so good!

Yep thats cerastium tomentosum.

If you pull a  piece away with a little root, you will have your own plant. Just keep it watered until it takes hold. Beautiful - snow in summer

I have one huge clump of this in my garden, only last week I took some cuttings and so far they seem to be holding their own. I didn't realise you could just pull a piece out with a little root it would grow. When I looked at mine it seemed like it grew out from 1 central root and as I didn't want to divide the plant I tried the cuttings.

That's what I love about this forum...you learn something new everyday 

Tattianna, I think that is the proper way to do it or divide the plant in spring. However, at a friend's house she told me to help myself to a bit and when I pulled pieces away close to the base of the plant, there was a little root attached to the pieces I pulled and they all took!

Yes Beware! I had some of this in a raised bed/rockery and within a few years that was about the only plant on it! It smothered everything. Beautiful, but keep an eye on it. I was busy with new babies at the time and let it just take over.

Brilliant - thanks so much for identifying that for me - and I will be careful with it!