Originally Posted by
corporate-wage-slave
Nationality isn't important here. What is important is the reason for travel. If it is to be with family and friends over Christmas, for example, that is unlikely to be a reasonable excuse under the legislation.
The poster said it is due attending to a health crises. They are therefore fine to enter.
Also worth noting that US citizens use the E-Gates at LHR so it is very likely they will not even encounter a Border Force Agent anyway to ask them.