I used to work at HomeServe, and if the AA cover is anything like it was at HomeServe, whilst issues like leaking pipes (which are causing damage, and unable to be contained, so not counting external overflows), are deemed an emergency, the boiler cover was breakdown, so even if your circumstances met what would flag you as an vulnerable (say if you were elderly, someone from HomeServe would be out with you within 4 hours, which was the emergency response time, even if the leak wasn't causing damage that wasn't containable), you would still be looking at 3 days at the best end of a timeframe (2 days if you're super lucky and it's an easy fix), as it was always next day appointments, the boiler engineer would have to attend to asses the problem, order the parts, which if ordered early may arrive the next day, but you're looking closer to another day, and then when parts arrive, they can repair it... hopefully (got so many re-attends when I worked there for still broken boilers)