Whether it is a general election, or a byelection, the elected MP has the same mandate. The party or coalition with the most MPs forms the government. The former PM was not elected by the "people', but was selected by his party's delegates. The new PM has been selected in the same way. Nothing has changed except the selection of a new MP. Labour received 33.7% of the votes in the last election. Hardly, a strong endorsement, nor much of a mandate. However, Labor won a majority of seats and a mandate to govern of 5 years. Nothing has changed. The mandate continues. The voters made their choice in 2024. Now they must accept the consequences of their poor choice. Next time, people who want to punish a political party will consider that they may instead be punishing themselves. Labour still retains a united and strong core support from the unions, the people who do well from the welfare state, youth and students and the migrant community. They aren't going to resign and give up an opportunity to push their brand of socialism.