How can I register as not fit to work?

ronnie123,
We'd need to know more about your circumstances to be sure, but the benefits I'd look at would be:

contributory ESA (this may apply if you've got enough national insurance contributions, looking at the tax years 2016/17 and 2017/18) ESA is employment and support allowance and there's a medical which looks at what work you could do - can be hard to get enough points in the medical so don't be put off & challenge the decision if you need to. You can backdate ESA by up to 3 months so you should ask for this if you could have claimed earlier but didn't

PIP (personal independence payment) - a benefit for the extra costs of disability. May apply if you have difficulty with any tasks at home (washing, cooking, dressing etc) or difficulty getting out & about out of the house.

UC (universal credit) - a benefit based on your income and overall circumstances. You say 'we have been surviving' so I'm wondering if you have a partner you live with. If so, it would have to be a joint claim for UC. You would have to explain your circumstances and eventually, they'd decide whether or not you have to look for work (hopefully not). Any medical assessment result you had for contributory ESA would count for UC too (for example if ESA decided you shouldn't have to look for work, that result should be applied to UC too). You can backdate UC for one month on the grounds of disability, so you might want to ask for that too.
Your savings will need to be below £16,000 to claim UC and below £6,000 to have no effect on your UC (for this rule, your partner's savings and yours are looked at jointly).

All sorts of issues can crop up with these benefits but I think you just have to start your claims and see what happens. 
In the unlikely event you weren't entitled to any of the above, you might still be able to get what are called national insurance credits for limited capability for work. 

To get things started:

claim contributory ESA here  (you will need to ring up the UC helpline eventually in any case to get an appointment)

claim UC online or by phone (online claim route is here)

Claim PIP by ringing up by phone (details here)

Don't be put off by any of the responses you get. You can claim contributory ESA as well as UC if you need to, but remember UC has to be a joint claim, whereas ESA doesn't. So you might want to claim contributory ESA first, along with PIP if you think it applies, and then have a chat with your partner about claiming UC. Citizens Advice can also help answer lots of questions you might have about claiming UC. 

The only benefit which is likely to come from the council in your situation is council tax reduction. This is to help you pay the council tax. Ask your local council about this and make sure you tell them if you have any changes in your income (including if you start getting any other benefits, like ESA, UC or PIP).

Will