Unfortunately the photo is a bit blurred, it might be common hemp-nettle, or enchanter's nightshade, or any number of other plants.

Ivy at the bottom of the photo, the rest is a horrible weed that's difficult to eradicate, has long, thin white roots that always break off when you try to dig it out. I don't know what its called though... hopefully someone else will.

I'm willing to bet the reason its all round the edges is because the roots have done under the stone edging and break when someone tries to weed it out.

Hi, it looks to me like ground elder, {Aegopodium podagraria}, see what others think, Derek.

Its not ground elder - I have to weed this stuff out all the time in a garden I still do, driven me mad for years... it has a tall, thin flowering stem with tiny white flowers on it, bit like heuchera flowers but not so tall

Got it, finally , after all these years - its Enchanter's nightshade, Circaea lutetiana... and where its causing me a problem is exactly the conditions it loves - heavy, damp soil in shade.

Maybe enchanters nighshade? (See question from Pdb on 28 April).

I agree Enchanters nightshade as yes its very hard to eradicate. But in a few years that ivy will have smpthered everything else...

I used weedkiller on this last year and it has worked pretty well but I'm pulling up any stray bits. If you visit the grave regularly you could pull it out each time but it won't get rid of it entirely.