As you're Irish, I'm sure you know SUI offer both the BCA and the FFS Option 1 bundled into one payment of ?85 per yer per person.
https://www.caving.ie/membership/
But if it's more than that which you're looking for, then I think talking to the insurance manager of BCA may be a good idea.
With you not owning a hut, it's difficult to know precisely what you want to insure against, but I guess it's the sort that pays out if you die, get maimed or lose an eye and your teeth. (and therefore cannot work).
The email address for the BCA insurance manager is insurance@british-caving,org.uk though I would read the FAQ fully before contacting them. https://british-caving.org.uk/wiki3/lib/exe/fetch.php?media=legal_insurance:faq_2019_05.pdf
(the email address was copied directly from the FAQ, it may have an errant comma)