The difference between the national proportion of votes and the number of seats is not due to first past the post vs proportional representation
In the UK we vote for each seat. That seat could be a clear majority far ahead of other candidates or it could be a relative majority.
FPTP or PR would just tweak the results but still end up with one candidate taking the seat
The overall majority of seats results in that parties leader being asked to form a government
The overall result does not mean that the party in government gets to make all the decisions
Parliament votes, and every politician in a seat (who has turned up that day*) gets to vote in parliament
MPs within the governing party should vote in line with party policy when it is a topic they campaigned for, (as directed by the party whip, but in practice can vote differently) but in all other cases they should vote in line with their local electorate (therefore you should be contacting your MP in advance of votes)
*assuming your MP turns up to parliament, goes into the house rather than the bar/public gallery, and listens to how votes are counted - Farage for example often failed to turn up for votes, then when he did turn up and try to vote he failed to do so properly and failed to be counted
As an aside, the first series of Auf Wiedersehn Pet showed an example of FPTP vs PR when they were choosing a colour to paint their hut.
FPTP - No body agreed on one colour
PR - They ranked all the colour options and the result was a colour that nobody wanted, but was the most common low ranking