I don’t know why you are not claiming benefit but the usual situation for an out of work, fit person would be to claim job seekers Allowance. If you subsequently become sick and get a note from your GP you become eligible to apply for ESA because jsa is no longer applicable.
Note that I say eligible to apply. A note from your doctor is not enough on its own, you don’t automatically get ESA and no, the DWP do not take your doctors word for it.
You would need to apply for ESA and send in your doctors notes. Initially you would go on the assessment phase. During this time you would have to complete the ESA 50 form which examines your illness in relation to a variety of work based activities. Each activity scores points (the poorer you are at it, the more points) if you score 15 or more points you would be awarded ESA and would no longer need sick notes, if you score less than15 points you are considered fit to work.
Eligibility for ESA is also dependant on NI contributions. But you can still claim if you have not paid NI if you do not have a working partner and have no savings/ other income