Is this normal for plum tree bark?

Definitely not normal, and this looks potentially very serious.
Immediately underneath the bark is the phloem, the cells that transport the sugary sap from the leaves to all the other areas of the plants including the roots. It looks as if you have lost all the bark, and probably phloem, on this side of the trunk for a significant length. What does the other side look like?  Is there any sticky gum/resin being exuded from the damaged trunk?
I'm certainly no stone fruit expert, so I hope someone else will come along with more information regarding cause and treatment.

That looks like canker  . I hope I'm wrong.

If I'm right you are racing to save your tree as it looks very close to ringing it. Pescadoris spot on in being worried.  To add to what Pescador said, your tree's vascular system is under the bark, if the bark goes all around the other side your tree will die. Google plum canker and have a look at the pictures and see if it looks similar to you.

We got a new plot this summer which had an apple with canker on it on the trunk so we've had some experience with trying to treat canker. You need to cut the diseased bit off to stop it spreading. Canker is highly infectious so you'll need to put something down on the ground to catch the pieces you cut off. These will need to be burnt and sterilise all your equipment afterwards. including your ground cover. We covered the patches with heal and seal to stop anything getting in afterwards.

Look up on you tube Huw Richards, how to treat canker, he's two excellent videos. He's treating apple trees, but it's the same procedure. If you google plum canker it's one of the 3 videos that come up.

Good luck.

It is defo not normal... but what is very interesting is that the branches of the tree look healthy  and quite normal. So here is a question for you ... is there any way a small deer,perhaps a muntjac , could have got into the garden ? Looks to me like something has nibbles at the bark but I am just guessing. We get a lot of this sort of thing happening in our gardens and it is usually caused by deer.

Ok will look it up. Thanks.

Does anyone know how it gets canker though? It’s fairly new, could it have had it from the supplier already, is it just had luck, is it bad conditions? I’ll do some tease arch soon. Thanks.

Fungus. It spreads via spores, although there is a bacterial form. Yours is most likely to be fungus. RHS is your friend, I'll put a quote and a link to their page on it at the bottom of my reply for you.
Do an internet search and compare the pictures to your pictures. It's really close.

Well what you need to be worried about primarily now is infection via you and water splash to the other plum and other parts of the plant. Think the common cold. Aerosol, rain splashs, or contact contamination aka your mucky paw. And you will get mucky paw if you use heal and seal- wear old clothes and gloves.
It's easily spread and it's in the natural environment already. It gets in via cuts in the bark. I'm not an expert but drought can cause bark to split if the tree gets too dry. And there was a rather dire drought last year so it probably got into your tree then and being under stress it's immune system would have been stymied because it wouldn't have had a lot of water to produce sap.

But how it spreads is why it is so important you sterilise your tools and why you have to ensure you catch all the prunings . If you leave a bit on the ground, it'll act as a reservoir to infect the tree again. You touch the bark with your hand then touch another part of the tree and you risk introducing spores to a previously uninfected area, causing another infection. Rain splashing on the tree will cause the spores to spread as well - why we went for heal and seal to keep the area clean. The rain infection vector is probably why it's having such fun going down your plum's trunk.

Ours probably got it from birds going from a very infected tree several plots along. It's an abandoned plot and the tree is a total poxy mess.

You need to cut it out and DO NOT STAB YOURSELF.  We wore safety glasses, had safety gloves, made sure we had a phone that was fully charged, Husband and I was up there so we had backup if stabbing happened. We also brought tea/biscuits as it was stressful. This is not a comprehensive safety list  but me sure of your safety. Do your tree surgery it when it's dry and preferentially been dry for a few days and look for dark spots in the living wood, get them out too. Those dark spots are the fungus having a good burrow into the wood. Look at Huw Richard and his Dad's video on You Tube, their how I know this to tell you.

It could have had it from the supplier, see what your supplier's returns policy is though because that is a really bad infection. Don't feel bad at having missed it as it's easy missed if you don't know what your looking at and you find out by encountering it.

I was working clearing the area around "our" new apple tree for several weeks before I heard someone on GQT asking what killed my neighbour's apple tree? Was it my pruning? The panel said there's a dark spot on the trunk and it's probably that rather than your pruning. That was when I realised hang on, there's a dark spot on the trunk of "our" tree. The "support's" tie had caused a rubbing wound on our tree which led spores in. Finger's crossed both our tree's live.

Feel free to ask all the questions you need, we just went through this in August.

RHS link
https://www.rhs.org.uk/advice/profile?pid=86

Here is their definition, there's a load more on their page. I advise you read it, they won't lead you wrong.

What is bacterial canker?

Bacterial canker is a disease caused by two closely related bacteria that infect the stems and leaves of plums, cherries and related Prunus species.

Cankers begin to form in mid-spring and soon afterwards shoots may die back. Shotholes appear on foliage from early summer.

OK, thanks all. Just adding a few more photos here, as when I lookup canker online its all a sort of red puss and I dont have that.

I think its about a year old and didnt cost much I am tempted to rip it out and get a new one. i cant find the receipt so cant remember where I got it from.