Your bike shop person is talking crap, it's unacceptable for a BB to fail within such a low mileage.
Don't worry about whether something is covered by a warranty or not, you already have the protection of the Sale of Goods Act and any warranty is just an additional benefit provided by the retailer or manufacturer. As the saying goes, "your statutory rights are unaffected".
Speak to your local Citizens' Advice Bureau for clarification of what you're entitled to from the retailer. They should not be charging you a penny for this fault, they should be apologising!
I'd tell them they have the option to repair it free of charge or I'll have it repaired elsewhere and chase them for the costs.
GC