I do not think there has been a government elected in the USA or UK with a majority of the people voting for them. A government is usually elected with well under 50% of all the people that voted. When one takes in the non-voters they actually have the backing of about a third of the electorate. Yet that does not stop them suggesting that they have a mandate to put their policies into practice.
A political party puts a series of policies into their election manifesto. When they get elected they claim that they have a mandate to implement them all. This is rubbish. I have never yet looked at any parties manifesto and agreed with everything in it. I usually have to settle for the lesser of two evils. I have to vote for the party with the least number of objectionable policies. That is not to say that I support all the things they put into their manifesto - far from it.
A government is not elected to purely represent its own followers. It is supposed to represent the whole country. To me this implies compromise and taking into account the people that did not vote for them (which is always most of the country).
So in Britain the Tory Party should presently be trying to find a way of taking into account the majority of the country (those who voted remain plus those who did not vote) who did not vote for Brexit.
In the States Trump should be taking into account the majority of the people (Clinton voters and those who did not vote) when putting into place his policies.
Clearly this is very difficult to do and many policies are not open to compromise but consensus is always better than imposition. Things are never black and white.