What are the tax implications of an American buying shares in a UK company?

I’m interested in investing in a UK based company that does not have shares on an American exchange. I had asked a question about if that was possible over here and since the answer was yes, I started reading about the tax implications if I were to by shares in a UK based company.

I found this on Investopedia:

Every country has its own tax laws, and they can vary dramatically from one government to the next. Many countries have no capital gains tax at all or waive it for foreign investors. But plenty do.

And this on what appears to be a UK government site:

If you’re abroad … You do not pay Capital Gains Tax on other UK assets, for example shares in UK companies, unless you return to the UK within 5 years of leaving.

That seems to be saying UK residents who are abroad and don’t plan to return to the UK within 5 years do not have to pay a capital gains tax. That is the closest I have been able to find to the rules for what an American needs to do.

I know that I will have to include any profits or losses on my US taxes like with any other investment, but does anyone know if a foreign investor has to pay some form of capital gains tax to the UK? And if so, is that taken out automatically on a sale of shares, or is there separate paperwork and payment that must be made?