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The UK can pursue a court case in the UK courts system.
If the amount is large enough to justify the expense, the UK can, under a process sometimes referred to as triple seal, transfer the case to the U.S. courts where a law suit is filed. The U.S. courts then rule on it, and if the issue is compliant with the laws in the court having jurisdiction over your location, then the U.S. court would serve the notice, and you can end up with levies and liens through the U.S. Courts.
The U.S. does the same thing. We pursue international tax evaders and criminals in much the same way.
In addition, if the UK were to bring a criminal case regarding tax evasion, they and the U.S. have an extradition treaty, so you could be extradited back to the UK if criminally charged at the level required in the extradition treaty.
Laymen who read the treaty contained at the link may misconstrue that it is only for certain violent crimes; but not that these are only singled out in the treaty to specifically state that these crimes are not considered politically motivated crimes. this is because politically motivated crimes are not extraditable. ALL crimes including tax evasion that could result with imprisonment of 1 year or longer are extraditable.
This extradition treaty also allows for seizure of assets and other property at the request of the extraditing country.
Now then...before you get real concerned, note that this treaty also limits extradition through the diplomatic process. What this means to persons who may face some crime in the UK of any nature, is that unless it is big, they are not going to use it.
I will tell you that I have not seen the Inland Revenue pursue tax cases to the United States for amounts less than $50,000.
I guess for you, what is important is knowing what they can do, as well as what they are likely to do.
I would not want you to make decisions under the belief they can not reach out and touch you, because they really can if they decided that they needed to.