Neighbour stealing my garden!

I would write a letter to him, marking it "letter before action", mention legal advice, attach the deeds (You mention the land registry, I'm assuming the land is registered and you have a title number? If so there is absolutely no worries about adverse possession, as it simply isn't as easy as taking the land for 10 years to make it yours) Give him 5 working days to remove his fence off your property after which you will take it down yourself.
Alternative: Would you consider selling the piece of land to him?

@fencedispute2024 that looks totally different to the original pic you drew!!! this new one looks like not only is the red bit yours but the bit should run all the way down to the back!!! can you take a screen shot from google maps. might be much easier!

FGS OP show him his deeds and yours, give him 48 hours to remove the fence. If he doesn't, you take it down. IT IS YOUR LAND.

Any developments @fencedispute2024 ?

Yes a diagram would be helpful of the house/ garden layout.

You need to get Official Copies of the Title Plan and Register. These can be used in a courtroom if needs be.

It’s not unheard of for the unusual division of land like this, but it does seem odd that it’s part of your garden and not theirs, especially at the front, but it’s difficult to picture from your diagram, obviously I understand if you can’t, but would it be possible to see a photo of it so we can see it as it is. In a way if I understand how it might look, it might make more sense to sell it or sign it over to your neighbours, but definitely get why you wouldn’t want that, I have my own experience of minor boundary upsets, nothing that escalated, but it could have done, in fact my dads garden could one day have a similar problem, so I get why you would want to stand your ground.

I can't really understand where the houses are or how that bit is in front of your house if the driveway is at the bottom of the pic. Can you draw a more detailed picture?

Clearly someone at some point bought or bartered for that, presumably bin-sized, patch. And I think it's more of a "patch" than "land". I would go in with him and get the paperwork changed so that these spaces make more sense, but allow him to pay for that and buy you a coffee. If you don't, then you're going to spend the rest of your lives tussling over who gets to use something that's only bin-sized. That's not worth the hassle.

Adverse possession can’t be split between home owners. He can’t just fence it off an claim it as his own after 8 years. And for adverse possession you have to prove you have been using the land. Title deeds are never irrelevant, it’s precisely for matters like these that they are needed.

If it is in front of your house, has he cut off your access for maintenance?

Solicitors straight away either direct yourselves or through legal cover on your house insurance if you have it.
Do not mess about
Do not remove his new fence, you could be done for criminal damage.
These things can drag on for years unfortunately

This is what I would do - it's weird to have that little bit extra as part of your land, do you use it for anything? I would get a solicitor to write me a letter stating that it is unequivocally yours as proven by land registry documents, but that you would be willing to sell to him for £X.

If you have legal cover on your household policy, call them for advice.
They can arrange for a solicitors letter to be sent to him

He can't claim as he's only been there 8 years and he has no evidence of it being used

I'd be removing it too.

I think he is a CF and he is going to claim adverse posession. He may try to argue that he and the previous occupiers of his house, have between them had unfettered use of the patch for 10 years. What your title deeds say will be largely irrelevant
I know solicitors are not cheap but you do need legal advice as soon as possible

I'm always amazed how it is on the 'victim' to try to maintain relations. Seriously he has been a dick and doesn't give two hoots about your relations

You may find the last house sale details still online. It may have some info or images that could be helpful.
Same for your house sale. What info did it contain and what images. It should stipulate who is responsible for what fences somewhere in your paperwork.

You may wish to look at some Google maps or older maps for images or previous building or sheds.

You may wish to look at any satellite images for other neighbour houses with a similar lay out for patterns.

You may have taken photos when the hedge was in place or in the background?

The fact that he didn’t notify you that he was planning to put up the new fence suggests that he knows full well that he’s encroached on your property. I’d never install a new fence without letting my neighbors know my intentions (we’re in a terrace so have neighbors on either side).

I’d follow @Snozzlemaid ’s advice first and then escalate to a solicitor if necessary. He sounds like a cheeky sod.

Do you need/want that bit of garden? If not I would find out how much the land is worth and offer to sell it to him. Obviously he would have to accept it's not his first though.

Is this the UK, and is your neighbour from the UK?

If so he will know what land registry is, tell him to go on there and search for himself. Then he won't be able to dispute the truth of the plan.

I would avoid solicitors until its the last resort, but do put it all in writing ideally get an email address and do it thar way.