Should I pay for importing my iPhone in the UK?

There are two main factors to take into account: where you reside and where you bought the device.

• UK resident, device bought in the UK: It was properly taxed already. If it was manufactured abroad, the retailer (or their provider) took care of importing it. Only issue might be proving that you did indeed buy the device in the UK.
• UK resident, device bought outside the UK (e.g. US): The device has to be formally imported (and dutied/taxed as appropriate). It's not allowed to import an item woth more than £390 without declaring it. If you go back and forth, you only need to pay once but you might need to prove you did in fact pay the first time around. If you didn't, it's entirely possible to get caught on a subsequent trip.
• UK resident, device bought in the EU: before Brexit this wasn't an issue, now the EU is treated like any other country in the world. That means two things: more thorough checks are possible when coming from the EU and you are much more limited in what you can import duty and tax-free from now on. However, a device that has been bought elsewhere in the EU before the end of the Brexit transition period should still be treated as a device that was bought in the UK.
• EU (or third-country) resident (that's resident, not citizen, it could still apply if you are British), device bought in the UK: no problem at all on the UK side but you'll have to deal with similar issues on the EU side.
• EU (or third-country) resident, device bought outside the UK: you're presumably on a short visit, if you will take the device back with you when leaving the country, you don't need to pay tax or duties (and usually don't need any paperwork). If what you bring will remain in the UK (it's a gift) then the regular import rules apply: £390 allowance (£270 if you arrive by private plane or boat), restrictions on alcohol or cigarettes.

As you are an UK citizen you return home with items you bought in the UK, you have already paid the taxes on them. It might be hard to proof it, as you likely did not take the paperwork with you.
If you have online banking and a payment that shows this phone or watch being paid in the UK, you can keep that or a print out of it handy.

If you bought your phone and/or watch in the EU before Brexit, you may try to argue that you have paid the tax while it was still part of the same system.

Next time you leave the UK with new or rather new expensive items, either take the paperwork from buying it, or get proof you did own it before you leave the country. You do not need to pay repeatedly for the same items.

As a foreign tourist you would normally not need to pay for items you take with you on travels, as long as you plan to take them out again.
Again, having an expensive item and staying long in the country you go to, like as a UK citizen who has the right to stay in an EU country, bringing proof you owned it before this travel will help.

New phones and watches do go down in value quite fast and the border officials will not blink an eye if you pull out a phone which is a few years old.

If you buy a new phone and watch and/or other things that take you over the limit you need to go to the red channel, tell the officer what you bring and how much you paid, and if you can not show paperwork, they may assume a value, and pay tax over what you bring in. If you do not go through the red channel, they may take it off you and still fine you. If in doubt, declare and they will tell you what you need to pay, or nothing.

These rules are now new between the EU and the UK but have been normal for years for travels from either the EU or the UK to other countries and what I write here is standard, learned over the years, no links.

Even if they are considered goods, You would usually be eligible for re-importation relief:

Goods imported in baggage

You do not need to make a formal customs declaration to claim relief on your own personal belongings re-imported in accompanied baggage if the conditions for relief are met.

These are usual rules but it strongly depends on the country, so you should still check the rules in detail.

Same principles apply to your phone and watch as to the clothes and jewelries you wear (but for certain jewelries many countries have special rules).

If it is an item from abroad brought in for sale in the country, it is usually an import subject to customs control. Gifts are also usually subject to customs control but usually with some exemptions.

If it is a restricted or banned good, it is subject to customs control and declaration regardless.

If you bring an item out of country and later return with the same item substantially unmodified, it is not usually considered a new import, at least for individuals.

If you bring an item for personal use as a non-resident and will leave the country with it, it is usually also not considered goods in the customs sense.

If you are a resident and bought a new item outside the country, it is usually considered an import and subject to customs control, even though if you used it already outside of the country as a replacement the customs usually won't care about it (this depends on the country).

If you are establishing or re-establishing in a country, your personal belongs are usually exempt but procedures differ.