This sounds like Domestic Flight Connections, you would be better off going over to the First Wing, there were some queues there yesterday too, but mostly in the 10-15 minute area. You can still claim the New York hotel cost under Right to Care, I suspect what the agent meant was that LHR customer services could not book the hotel. Right to care absolutely is payable in bad weather. You probably have a basis for IDB compensation too, keep your boarding pass safe.