There are three main provision of the laws that might cause you problem and they all involve exporting to the US or encouraging others to do so. The primary statute on point is 35 U.S.C. 271(a)-(c).
(a) Except as otherwise provided in this title, whoever without
authority makes, uses, offers to sell, or sells any patented
invention, within the United States or imports into the United States
any patented invention during the term of the patent therefor,
infringes the patent.
(b) Whoever actively induces infringement of a
patent shall be liable as an infringer.
(c) Whoever ... imports into the United States a
component of a patented machine ... for use in practicing a
patented process, constituting a material part of the invention,
knowing the same to be especially made or especially adapted for use
in an infringement of such patent, and not a staple article or
commodity of commerce suitable for substantial noninfringing use,
shall be liable as a contributory infringer.
Thus, if you import an infringing product into the US or induce someone to import the infringing product into the US, then you can be held fully liable as an infringer. Even if you are selling through a third party distributor, you likely be seen as inducing the importation depending upon the facts.
There is nothing illegal about selling to US customers when they are in the UK so long as that sale is not part of an import scheme.
Now, there are some procedural issues that a patentee would need to overcome: (1) can a court get jurisdiction over you as a non-US entity; and (2) can they collect money damages since you are in the UK. These are big questions. If the case is brought in the US International Trade Commission (USITC) rather than in court then the court automatically claims jurisdiction based upon the imported products. The nice thing (for you) about USITC cases is that USITC never awards money damages (only awards exclusion orders to block further imports). If you lost a money judgment in court, the patentee could seize your US assets. There is no particular treaty between the US and UK on enforcing foreign money judgments. However, it is usually relatively simple for a US judgment winner to go to the UK and collect the money.