@Sarah thankyou
Your local authority too, they tend to have similar working contracts and patterns as local government.
I know someone that works for Bupa recruitment (she had no prior experience in recruitment) and she works from home for most of the week but she mentioned a few ladies on her team work part time with working from home, so some weeks they didn’t have to go to office at all
I’ve you don’t mind driving to Sheffield, have a look at the civil service. I work flexibly including flexi hours, condensed hours and working at home 3 days a week. Been working in the service for 13 years now and it’s very family friendly. Most of my team are parents, working around their caring commitments.