That'll teach me to buy something really cheap.
The purchased battery wasn't in a sealed bag, so might have been 'previously enjoyed'... and it lost its charge faster than the phone's original battery - and, once it was flat, it died completely.
They posted me a replacement very quickly, after I sent an email; the second replacement is marginally better than my original one... I'm uncertain whether the replacement is also a 'used' battery, also having arrived in an unsealed bag.
Speedy after-sales service, but perhaps better to ensure that you pay more for a genuine, new, battery.