Britain elects a Parliament, and a prime minister needs the confidence of the Commons. A governing party can change its leader without a general election. That is a feature of the system, rather than a loophole discovered by politicians we happen to dislike.
It doesn't follow that every new prime minister can claim a fresh personal mandate for a substantially different programme. Legal authority to govern and a claim that voters asked for a particular policy aren't quite the same thing.
What an election asks people to choose
Modern campaigns place enormous emphasis on the leader. Their judgement, promises and character are central to the offer. When they leave office, voters are sometimes told that none of that was what they were formally choosing.
The constitutional explanation is correct. It doesn't fully answer the political objection. If the campaign invited people to choose a leader and a programme, replacing both can change what they reasonably understood themselves to be supporting.
The handovers after the 2019 election made the tension particularly visible. Boris Johnson was succeeded by Liz Truss and then Rishi Sunak before the next general election. Each could govern through parliamentary confidence. The degree to which either inherited public consent for a different programme remained a separate question.
Authority isn't a blank cheque
A mid-term successor needs room to respond to events. No government can promise that circumstances won't change, and calling an election every time a leader resigns would have costs of its own.
But there is a difference between adapting an existing programme and claiming that winning MPs' support authorises an entirely new offer on behalf of the electorate. A prime minister should be honest about which they are doing.
Anthony Eden called an election soon after succeeding Churchill in 1955. That doesn't establish an unbroken convention that every successor followed. It does show that seeking public endorsement is an option, rather than a constitutional impossibility.
My preference is that a leader who substantially rewrites the programme should seek a mandate for it. They may be legally entitled to continue without one. They shouldn't use that entitlement as proof that the public has already agreed.