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The official UK document says:

You can bring in other goods worth up to £390 (or up to £270 if you arrive by private plane or boat).

If a single item’s worth more than your allowance you pay any duty or tax on its full value, not just the value above the allowance.

The question:

Is the tax-free allowance applicable per an individual item or per total cost of all items combined in a baggage?

If you need a more detailed example, here it is.

I am relocating to the UK and going to take my desktop computer with me. I want to disassemble it and put small parts into my backpack and big parts into a suitcase that will be put into aeroplane's luggage. All these parts will be with me upon my arrival to the UK.

As for the computer. I bought all its components separately in my country and put them all together and used the computer for around a year. Almost all the parts in the desktop were cheaper than the tax-free allowance except the Video Card.

What will I be charged for? For the sum of all the components prices or only for the video card?

To answer your stated question, it is the total of all the goods. Imagine I have an item that costs 100 pounds. If I want to bring 5 of them, that is 500 which is over the limit. So taking something apart or opening a package will not normally reduce your duty in any way.

The thing about the single item suggests that a small trick may be available: a single 500-pound item would pay duty on 500 pounds, but 500 1-pound items might only mean paying duty on the excess items for 110 pounds. Before I tried such a thing I would check the duty rates, which could be different for computer parts than they are for computers that are fully assembled. Also, many border guards just wave you through when you have a little over the limit, but if you irritate them (by making them count 500 items, for example) they may get nitpicky. I would definitely file this under "advanced techniques."