How would he get carers allowance? She'd have to be claiming herself and she earns far too much to do qualify. She's also travelling extensively so wouldn't be eligible given how strict the criteria is.
Apply for Carer's Allowance - money to help you look after someone who needs to be cared for. Apply online or use form DS700.
www.gov.uk
He probably works minimal hours or not at all because she earns enough to sustain them. He was an admin worker so his salary wouldn't be comparable to her earnings.