At present in the UK, should a prime minister be removed from office (either by resignation or made incapable of fulfilling the office due to injury, illness, or death) the party forming the government simply elects a new leader.
Of the 24 times we've had a new prime minister in the UK since 1916, twelve of these occasions happened without a general election, and only five of those went on to win a general election during their term. This leads many in the press and opposition parties to claim that the new prime minister has no mandate for many of the policies they choose to enact (an example being the manner in which Theresa May is approaching the UK's departure from the EU).
What changes would have to be made to British law to change this process? Would a simple act of parliament be sufficient?