Couple of things to mention.
It's not called the "emergency lane", it's the hard shoulder.
The US typically has lots of wide open flat freeways - if you broke down you could easily pull off onto the grass.
The UK's motorways are typically bordered by steep sides - if it wasn't for the hard shoulder there would be nowhere for broken cars etc to stop except for live lanes.
Example:
The hard shoulder can also be used for the emergency services to get through in the event of a large traffic jam - the UK's motorway network is a lot more congested than US Freeways, so jams build up a lot quicker if theres an accident.