[AB-UK]

There may be an exclusion in the warranty terms relating to battery issues not caused by a manufacturing defect.

You could get some legal advice - is the CAB still operating a service?
Not fit for purpose is one issue (the Start/Stop system).
Refusal to honour the warranty is a second issue.

If the dealer still refuses to fix the Start/Stop under warranty, and the advice is that the dealer's refusal is spurious, have it fixed by an independent Volvo expert, then you could take out a Small Claim against the dealer to have the expense reimbursed.