Is the cut end turning dark brown or blackish?
If it is still white, cream, or beige, it isn't in serious trouble. I would just rub some ground cinnamon on the end and move it to a drier area, to prevent future problems.
If it is darkening, a rot fungus is taking hold, and you may need to use a systemic fungicide. Here in Arizona, I would use propicanazole, but I don't know what would be legal in the UK.
For the future, rub a bit of cinnamon on the cut ends of any succulent cuttings, and let them dry out a few days, before planting them.

I have added a pic showing the end in question. I appreciate the response but respectfully isn’t Arizona one of the driest places on the planet and England one of the wettest.
Perhaps I should bring it in to the glass roofed conservatory where it will still harden up as it’s unheated but it will also get a chance to dry out? Before I act on any responses I may get suggesting I seal it with wax?

I'd bring it indoors as it is very wet. let it dry out and see how it goes.

the sealing with wax is done by the commercial growers and is partly so the growers knows which end is the top of the cutting. it will prevent bacterial infection but it is done at the time it is cut. if you seal this you will just seal in any bacteria/fungi that is already present.

welcome to GoY too.

Another option is flowers of sulphur, which works well on most succulents. You should let the cut surface scab over and become quite dry before planting. Then pot into a coarse dry compost until roots are well established. (So keep it under cover for the rest of this winter)

Whew, Zedd! That cut end looks bad. I would definitely put it where it won't get rained on, at least. On the other hand, that new growth looks pretty healthy, so it can't be as rotten as it looks. With luck, once it is kept dry, the end will become corky over the next few weeks, and can then take a fair amount of rain. That species, Yucca elephantipes, is a subtropical, rather than a desert Yucca, and can take more wet than most.
Yorkslass' suggestion of sulfur dust is correct. It is actually more effective than cinnamon, but it may be a bit much to go to GC for a pound (1/2 kilo?) canister just for a cutting or two, while most have a little cinnamon on their spice racks, ready to go. :)

Well I didn't know you could use cinammon so its useful info all round!

That’s great. thanks so much for your responses.
Yes the new growth from what was just a stump (without roots) 1 ft mid section of a tall plant appears healthy.
I have now brought it in under a glass roof so it still gets plenty of daylight but is unheated and almost as cold as outside. I shall keep an eye on it and hopefully it shall dry out over the coming months I reckon rather than weeks.
Regarding the cinnamon, shall I just sprinkle a teaspoon of the ground variety over the what appears less than solid soft cut open end?

I'd put a quarter teaspoon or so on a puff of facial tissue, and just sort of poof it on the stump, like old-fashioned makeup powder. Same way for dusting sulfur.