I do not know whether you accept that you are not entitled to JSA but you may find this calculator useful. It is easier to read than the government one.
assuming that you are not, the situation with the insurance company would depend on the terms and conditions of the policies.
Sometimes it is covered and sometimes it’s not. I spoke to a gentleman I know who is a director of such an insurance company (not one of the ones you mention) and he confirmed to me that their view is that they would expect you to take a position if the salary that you are being offered was 85% or more of the salary you had previously enjoyed.
I don’t know whether you went directly to the insurance companies or went through a broker but it would be worthwhile contacting either the insurance company or the broker to get their underwriting view on the payment of the claim and what their expectation would be.
If either of the insurance companies says that they will refuse to pay out if you don’t take any job, then you have a substantial complaint to make to the Financial Ombudsman Service. Before you complain to the Ombudsman you have to have exhausted the insurance company own complaints procedure. It would clearly be unreasonable for the insurance company to expect you to take a job which paid less money than the benefit you were currently enjoying because, if they did, they would expect everyone to take low-paid jobs purely to escape paying.
Can I clarify anything for you?
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