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It's really clear (I mean, more than that the EU referendum was just advisory clear) that you are voting for a candidate, not a party, because that is one of the defining features of the First Past the Post electoral systems.
If the MP dies in office, then the seat is vacated, if you voted for the party, the party could just replace them.That people don't understand this should have been a warning for the EU referendum.
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Is that neccesarily the case? Surely it depends on a personal decision of the voter. Some will vote for an MP because they believe they will do a good job at representing their local interests on a wider scale and therefore are voting for the candidate and their policies and promises on a local level. Others may vote for a wider idea of trying to get a party into power as they follow their overarching policies and believe that the government should be run by the party of that MP. Plenty of people vote for an MP that they do not agree with in order to get the party in to power no?
If you resign from the party for which you stood, and were duly elected, there should be no continuity. There should have to be a bye election/re-run to give the electorate an opportunity to confirm whether they were voting for a candidate or a party.