If enough Members of Parliament defect causing a Government to lose their majority, is the process that the incumbent can try to form a new Government via coalition or confidence and supply? If this fails must a general election be called?
Losing a majority doesn't do anything in itself. However, a Vote of Confidence would likely be held by the Opposition. If the government wins that, owing to support from minor parties, absentees, or the like, it remains in office, although at risk from another such vote.
When a government loses a confidence vote, it has a chance to form a coalition, or otherwise obtain support, if it wants to try. Under the Fixed-term Parliaments Act 2015, it has 14 days to pass a vote of confidence. During that time, another party or combination of parties can also try to form a group that has a majority. If no vote of confidence in a government is passed before the 14 day deadline, a general election is held.
The current agreement that the Democratic Unionist Party has with the government commits the DUP to supporting the government in votes of confidence and on spending bills (that's "supply"), and on some other issues, including Brexit.