> In the US there have been other parties that have put presidents in office
There have never been more than two nationally-competitive parties in the US. There have been times when a party collapsed and subsequently was replaced (the Federalists by the Whigs, and the Whigs by the Republicans.)
> Theodore Wilson was a Progressive Party candidate
Presumably, you mean (former) President Theodore Roosevelt, who, formed the Progressive Party in a factional split from the Republican Party over his dissatisfaction with his hand-picked successor.
And who didn't win, so isn't an illustration of your claim that parties other than the two major ones have put Presidents in office.
> and in the UK, which also has a first-past-the-post system, there are multiple parties and the country is currently governed by a coalition of Conservatives and Liberal Democrats
The UK and US differ in that, in additional to FPTP voting for members of the national legislature, the US has a separately (and indirectly) elected strong executive using a means that is even more strongly favors the two major parties than simple single-member district FPTP elections do; this not only gives a greater tendency for a major party to win control of the administration by winning the Presidential election, it further limits the expected influence of non-major party candidates for the national legislature, which further reduces their prospects.
So, yes, there is a well-understood structural reason in the electoral that the US has even less representative government and a stronger tendency to a two-party system (even though it has weaker parties) than the UK, even though both use FPTP for the national legislature.