Hi,I have recently noticed quite a few of these shoots springing up in my lawn

Doesn't look like ground elder to me. At first glance the one on the left almost looks like a fuchsia. Weird.

Do you have a cherry tree near by? they remind me of suckers from that. but not ground elder.

They do look like suckers. Have you looked at neighbouring gardens to see if there's anything similar? I would be to inclined to take out a turf and try digging them out to see whether they are on their own roots or are connected with a longer root from somewhere else. Looking at the stem half of it seems to be last year's growth. As a last resort more regular mowing will prevent them coming to anything.

Agree with Seaburngirl, mostly likely growth off roots from a cherry tree somewhere. These often continue to grow even after a cherry tree has been removed - the trouble with cherry trees is, they put out a lot of long surface roots over quite a distance... If the cherry tree is in your garden and you want it, you can't poison the root to stop this happening.

Thank you for your comments.
I do have a Cherry Blossom Tree (non-fruiting) which is quite large.
I have also had a plum tree which we have recently had removed.
Iain P

that looks like the roots of either the cherry or roots from the plum that was removed. keep mowing over them just in case they are the cherry.

Thank you for all your comments, I guess I’ll just keep on mowing.