Is this poplar/willow the roots run along way? if so it needs to be pulled up as you see it. I hope its not as it can be a nightmare. Best thing is too ask the neighbour what sort of tree it was, then you can get better advise.

Thanks - well, I know it's neither poplar or willow. When you say 'pull up' - I've digging to roots out which is bl**dy hard work (and makes a mess). I had heard that you just have to cut the sprouts as they appear and wait for it to die off>

Could have been an ornamental cherry tree - these do spread shallowly through the soil for some distance and try to grow. Remove what you can as you are doing - if you continue cutting any growth off, it won't stop it coming back, I'm afraid. If you have large roots that you cannot get out, buy a bottle of SBK, use a medium wood bit on a drill, drill shallow holes into the root and fill them up with the SBK (without getting it anywhere else, including on yourself) and cover with something. SBK is a brushwood killer and should deal with these roots if you put enough holes in.

Well, the stump's been removed and all these sprouts are coming from long tendril like roots below the surface of the lawn, typically 1cm-2cm diameters, down to quite thin, so can't really drill into those?

Well if they're that thin, you should be able to heave them out and repair the lawn afterwards.

You need to let the growth grow big enough to spray with SBK. Cut out a piece of polythene and place it around the unwanted growth, cut a hole in it, pull the leaves through. Spray and then wrap the polythene round the leaves, tie up and leave it to work.

Seems like Rhus to me. We had the same before and after our back neighbour got rid of his tree as it was bobbing up all over his garden. Long before he gave it the chop, I was cutting the bottom out of large lemonade bottles, discarded as litter, placing them over the shoots and giving a squirt of something noxious through the neck .He complained the tree had stopped making those candle thingies......wonder why?