There isn't actually register of unemployed people, per se. The only figures that are recorded are of those seeking benefits. (So if, say, Richard Branson was to step down from all of his company roles, he couldn't be counted as 'unemployed' while he was seeking something new).
That actually makes sense as there are plenty of people who're only 'semi-unemployed' or 'part-retired' (such as me), who aren't claiming benefits but aren't desperately seeking employment either.
If you've got a recent full record of National Insurance payments though then, as long as you're actively seeking work, you'll be eligible for Contribution-Based JSA for up to 6 months, as it's NOT means-tested. (If Richard Branson was thrown off the boards of all the companies he's currently on then, as long as he was actively seeking work, even he would be eligible to receive it).
People who aren't eligible for Contribution-Based JSA (either because their 6-month period on it has finished or simply because they've not made enough National Insurance payments) can apply for Income-Based JSA but that IS means-tested.
(To the best of my knowledge, the statements above still apply to the relevant elements of Universal Credit).
So it might be worth applying or Contribution-Based JSA (or Universal Credit, as appropriate). Start here:
https://www.gov.uk/jobseekers-allowance
I hope that you do better in job-hunting than I did when I was actually seeking work. Over 2000 job applications resulted in fewer than 100 letters (or emails) back. From those, I got just three interviews.
One firm told me I'd got the job subject to the approval of the 'big boss' when he returned from holiday. When I heard nothing from them for a while though, I phoned to ask about the job. They then told me that the big boss had decided that there wasn't a vacancy after all (yet they'd not had the courtesy to tell me).
Another firm invited me to do a day's unpaid work trial. I worked from 5am to 6pm, with no real breaks, and thought that I'd done OK. However I never heard from them again.
I was also invited to do a day's unpaid work trial at another firm. The boss seemed really impressed at the end of the day and asked me to come back the following day (paid) to help him complete some tasks that he's spent many months working on (but which I'd largely got sorted out, while working at other things as well, in just one day). After I'd not heard from him for several weeks though, I wrote to enquire about my pay (for the day's work) and the job. I receive a cheque and a very apologetic letter, saying that he couldn't employ me because I was 'too intelligent'!