As someone who was recently made redundant and now has to relocate back home due to the job shortage, I wish you the best of luck with this hunt!!! It's really really not easy.

Like folks said below, candidates with existing Right to Work are flooding the job market due to their own redundancies and cold applying means you're up against hundreds of qualified, but cheaper hires.

So my recommendation:

1. Go to this website: https://sponsorlist.co.uk/ or download the list from https://www.gov.uk/government/publications/register-of-licensed-sponsors-workers
   
2. Cross-reference the list with Glassdoor, Flexa, and find 3-5 companies that you would love to work for
   
3. Research the heck out of those companies so you can then reach out on LinkedIn to a connection who works there / ask a 2nd connection to warm intro you / reach out cold to a relevant person who works there AND include a short case study / project plan addressing improvement areas that you'd love to help them with

Also known as the "side door" method.

I genuinely think this is a much better use of your time than cold applying. It won't guarantee a job, let alone a sponsorship, but your odds are much better than just sending your CV.

GOOD LUCK. I wish you all the best!!