New Job benefits

Hello, just need a little help to see what options are available.

I currently work in an office job and have recently gone part-time for medical reasons, while looking for new job which would suit me better. I've found a job and the employer seems very interested but it would mean less hours and less money than what I earn currently.

Basically would I be able to apply for Council Tax/Housing Benefit if I fall into the guidelines for it? Or will they simply say that I chose to take a different job so I can't get benefits for it. It's in no way redundancy or being forced out, but my long-term health is dependant on finding a job closer to home and one that I feel I can cope with.

Thanks in advance.