I live between the UK and Argentina, but I am only a legal resident in the UK. I have a LTD company in the UK which I used to purchase a laptop (~4000USD) in New York (travelling Buenos Aires to New York return) – now I am travelling back to the UK I am starting to consider whether or not I will be asked to pay tax on this laptop to bring it into the UK.
You should have to pay tax in the UK for any personal possession you bring into the country for which you have not paid UK tax before, over a certain threshold.
A $US 4000 computer is well over that threshold.
The way not to pay double VAT (or whatever the local tax is called) is to claim it back or arrange not to pay it in the country you buy said item. Like in the tax free shops in the airport you leave from.
The UK does not get any of the foreign tax and is not concerned with you paying double, it is up to you to avoid paying outside the UK. And the UK is not special in this, all countries I know about have this tax on arrival with foreign bought goods.
We have a question at this time about traveling into the Netherlands with a used wedding dress, tax plus extra fees coming to over €1000.
The right thing for you to do upon arrival in the UK is to use the red channel, something to declare, and talk with the officers there. Have proof of the price handy, in case they evaluate the price higher than it actually was. Paying tax in the airport means that you will not run into trouble should the tax people check your company for whatever reason. (I am neither in the UK nor knowledgeable about the UK tax people but I have heard some stories how intensive those checks can be.)
If there is an exemption for business use/purchase the officers will know and implement it, on the other hand, if you have to pay more for it not being a person possession they will know that as well. I can not help you in that.
There are many people who just use the green channel and act like they did buy the computer 'at home' before their trip but as Stack Exchange site we do not tell people to break the law.