Accidentally left luggage abroad, and it's going to get shipped to me by a friend. Do I need to pay customs on getting my stuff back?

The rules are complicated: See https://www.gov.uk/bringing-goods-into-uk-personal-use/arriving-in-Great-Britain

If your items were originally purchased in the UK or the EU (and not in the US) and you didn't establish a second residency in the US, then typically there is no customs due. However the rules are complicated and you may have to prove somehow that the goods were originally acquired in the UK.

I recommend compiling a list of the items, guestimate their (second-hand) value and list date and place of purchase (as good as you can) and then send this to the shipping company and ask for advice. Shippers have a lot of experience in filling out customs paperwork.

Moved here as requested above. I think the procedure i called "Returned Goods Relief" and I think the info in this link supplements the info & link posted by Hilmar. From link, about half way down: "You can claim Returned Goods Relief in the normal way, orally or by conduct (walking through the green channel). If you are sending your items by freight you should claim the relief by using the customs procedure codes in the Tariff." https://www.gov.uk/guidance/pay-less-import-duty-and-vat-when-re-importing-goods-to-the-uk-and-eu

When I was traveling with my wife, we needed to mail back some of our luggage both from Japan and from USA to Poland. Our customs are known for applying fees whenever they can, but they just let both cartons thorough, seeing obviously used equipment (incl. rehabilitation equipment they reclassified on their own to "child toy"), souvenirs and clothes. YMMV especially since you no longer are in the EU.

Some advice that should work no matter what country you are in:

1. Obviously used clothes, if they are not of premium brands and obviously belong to one person or one couple, can be declared as worth $0 and I never heard it causing any problems.

2. Souvenirs are usually easy to estimate and cheap, and I'm yet to see anyone asking for a receipt, including absurdly meticulous Japanese post office.

3. Do list everything that's in the package. Making life easier for customs officers can't hurt your case. They are people too, they want to make life harder for smugglers, not forgetful citizens.

4. Do listen to your shipping company, they know what they are doing much better than you do. If there is a shipping company that specializes in your specific route, use it. For example, we used Polamer Inc. on Poland - America route.

5. For sporting and outdoor goods, and tourist equipment like selfie sticks, if you bought online you still have email confirmation. If you paid with card or wire transfer, confirmation of money transfer from your bank + your statement that "this paid for item X", and https://archive.org/ website snapshot from around that date showing prices similar to what you paid was enough for everybody so far. Everything we mailed was visibly and obviously used. Import laws pretty much can't require receipts as not every country even uses such a thing, so you are free to prove the value and ownership in other ways.

I once forgot a pair of jeans by my friend in the US, which I had just bought there. They cost a fortune in customs on entry to Denmark! I guess because they were brand new. Later I sent from the US an Amazon Kindle e-book reader to Denmark. I unwrapped it and did my best to make it seem used. It got through customs for free. -- Bottom line: It's a game.