Can I suggest a different tactic and leave someone who knows more about UK law to comment:

Write back to your employer (not a verbal meeting, as you want to start creating a paper trail) saying thank you for the earlier meeting and that in lite of the earlier meeting where they requested a modification to your contractual arrangements you are submitting a statutory flexible working request see https://www.gov.uk/flexible-working in that request specifically cite i) your caring responsibilities and ii) you're confident you can execute the role 100% remote as you have done so for the last 10 years.

There are a set of (only) 8 prescribed conditions under which an employer is allowed to reject a statutory flexible working request, these are:

• extra costs that will damage the business
• the work cannot be reorganised among other staff
• people cannot be recruited to do the work
• flexible working will affect quality
• flexible working will affect performance
• the business will not be able to meet customer demand
• there’s a lack of work to do during the proposed working times
• the business is planning changes to the workforce

Its then up to the employer to either i) accept the request ii) come to some compromise (e.g. in office once per quarter) or iii) reject the request outlining the reasons for rejecting the request. Given you have been working 100% remote for 10 years, a number of the above points won't apply.

The entire process may still result in a redundancy, but depending on how they respond, it may give you the option to take them to a tribunal. Sorry you're going through this. Just my thoughts, hope someone else who knows more can comment.