A private members bill to bring in home education registers had its Second Reading in the House of Lords on November 15th 2024.
The bill has zero chance of becoming law not least because the government has its own legislative proposals in the Children’s Wellbeing and Schoos Bill, read more here https://edyourself.org/childrens-wellbeing-schools-bill/
Parliamentary sessions are explained here as usually lasting for a year. The current session began with the Kings Speech in July 2024.