Depends how long your roses have been planted - if its more than 3 years, I wouldn't recommend digging them up. Ground elder can be controlled or checked by using glyphosate, mixed as a SPRAY and only applied to the foliage, preferably on a still day to prevent spray drift onto the rose foliage or any other plants nearby. Best done in mid summer. If your border is bounded by a path or hard surfacing, it will be next to impossible to dig out all the ground elder even if you did remove your roses and dig, because the roots/rhizomes will be under the paving - same applies if its coming through from next door.

You can certainly dig out what you can now, and then let it all grow on and treat next year, link below

https://www.rhs.org.uk/advice/profile?PID=215

I agree with Bamboo except that I would don a pair of rubber gloves and use a sponge to rub the glyphosate onto the worst weed I have ever had in the garden.

If the rose bushes aren't too big, then I would do as Bamboo suggests but I would get some large black waste bags and cut the tops out. Slide the bags over the rose bushes and tie at the bottom. This way you won't get any drift on the rose foliage. I would do it now but I wouldn't dig them out, rather let the glyphosate deal with them.

To contain glyphosate & prevent overspray. Cut a 4 pint plastic milk container about 1/3 down. Use the handle to place over weed & spray through the pouring hole

I got rid of mine with Roundup Weedkiller Gel Spot Treatment, it was a very Tedious job but it worked in the end, have to have a lot of patience as there was a lot of it LOL

I painted mine with Roundup . . . back-breaking, but it has worked. Obviously, it might come back at some time, but fingers crossed . . Good luck Holly!

I like the Gel spot treatments like Lady Essex. You don't have to worry about spraying other things, and its easy to apply. That's what I use. I have Ground Elder as well. Its sometimes fairly easy to pull out by the root if you have dry , light soil. But it always comes back.

I've heard one can eat the young leaves, never tried them though & can't now as mine is all gone as my way worked. LOL :o))

Sorry I am late in acknowledging you all but I used to get an e-mail when my question had been answered, doesn't seem to happen now.
We do have some Glyphosate so I might us the black bin bag idea then spray. I could then, perhaps, use Scotsgran idea and just dab the leaves that are very close to the roots.
Thank you all for your suggestions.