Deliberate age discrimination is no longer legal; so all jobs, full or part-time, have to be advertised to everyone.
If you’re looking for something local check out your local newspaper, or area free-sheet – it’s always a good idea and most now have an online version to make things quick and simple.
All the major national papers have job sections, and all are online – so if you’re looking for part-time employment, your first port of call should be the internet.
The Daily Telegraph usually runs a recruitment section on a Thursday in the printed version, but you can visit the online section in their website any time you like: https://Jobs.telegraph.co.uk has a simple search facility, so just enter Part-time and up comes a huge selection – nearly 21,000 last time we looked!
The Guardian came up with a smaller number of jobs, just over 2,000, but allow you to home in on the specifics more quickly
https://jobs.theguardian.com/jobs/
The Times search facility is less straightforward than the other 2 papers, appears to carry even fewer part-time posts, but they do seem to cover more senior appointments. Always worth a try, you’ll find them on
http://appointments.thesundaytimes.co.uk/jobs/
They also feature the Times Top 50 Employers for Women, which gives a useful indication for those looking to apply directly to potential employers.