How would the U.S.A. react if the U.K. became a communist Islamic state?
I'm going to violate my usual policy of downvoting and/or reporting this sort of question, and give the questioner the benefit of the doubt by assuming that this is a sincere question, but they're simply confused.
Simply put, the scenario you describe is by definition impossible. Communism is fundamentally about overcoming the conditions that produce religion (cf. the introduction to Marx's A Contribution to the Critique of Hegel's Philosophy of Right). This does not mean that religion will be repressed by the state, à la the Soviet Union under Stalin and his successors (when they weren't making common cause with the Russian Orthodox Church, but that's an aside); however, it does mean that the "state" (I use quotes here to signify that the central authority of the post-revolutionary period will not be a state in the mold of modern bureaucratic states) will be much more secular than current states, and will not privilege any religion over any other, not merely be prohibited from establishing a church and committed to a largely formal religious pluralism. To describe any polity or social formation as "Islamic" implies that it somehow embraces Islam as being central to its self-conception; modern communism can't do this. Such an establishment is contrary to its most basic principles.
There have to be so many financial relations and cooperations between the UK and the country that evolved out of its early colonies that we would experience a enormous reorganisation of capital wealth and power, if the UK would turn to an communistic ideology or government.
If the UK would become islamic, this fact would not disturb the economy too much, as we can see according to the trades with Saudia Arabia and other islamic profitable countries.