Looks a bit like Hebe pinguifolia 'Pagei' but not sure. I have found that Hebes are best pruned on a regular basis so not to let them get too big for the variety. You have too much dead growth so you could dig it up, reduce by half or go for broke and cut down to a couple of inches above ground and see if it regenerates. Personally, I would dig it up a replant with something else that takes your fancy. If you do want to prune, then I would do it now and not later in the season.

Hi again Meld. The Hebe should regenerate in time. It sounds as though you didn't try getting rid of all the Carex.There is no point in doing much else until its all gone. As say you are a novice gardener I'd advise you to do what has been suggested by the other people who have had similar problems and dig out that thug before doing anything else. It will be a number of years before you can get rid of it all completely but just cutting it back will be a very temporary solution and it will be back next year and bits will reappear for several years to come.

I ignored advice not to plant it a long time ago and am still regretting I didn't listen. Treat the thug with no mercy and in the meantime don't do any perennial planting near it. If you need to get started with young shrubs and perennials you can always grow them in large pots until the ground is cleared, but for next year at least I'd strongly advise you to stick to annuals in the ground until you can see the extent of the problem.
Whatever you do, don't let it flower.

Hi Steragram. I have cut off all the growth on the sedges and am finding a few plants completely smothered by them. As people have previously commented on how difficult they are to dig out I am going to try and kill them off with weed killer. The root balls are huge 🤦🏼. 🤞it works. I'll hang fire on cutting back the Hebes until the spring. Thanks again for all your advice. I'll try and attach some before and after photos

Hi Meld that is a hebe and it will regenerate if you cut it down by 2/3 but wait until spring.