I think you should be able to ask them why it's cancelled, as this determines your rights to compensation/care.
Assuming BA can't wriggle out of it, they're covered by the EU regs:
http://europa.eu/eur-lex/pri/en/oj/d...en00010007.pdf . €300 if they get home within 4hrs of scheduled time, €600 otherwise plus transport LHR to LGW (or another agreed point).
Maybe if you point this out to BA they'll come up with some better options? There's space on evening flights from Philadelphia and DC if they don't mind the detour, but yes NYC looks full.