How much to fix?

Well, I suppose the rattling is most likely that part of the exhaust... Probably worth taking it to a garage where they can lift it and have a good poke around. Don't forget to send the bill to Essex County Council.

That bill will only be able to be claimed back if some nice person reported the offending pothole 2 (?) days or more before the incident, and normally the type of road (main, side, country lane etc) may also be pertinent, because it would depend upon whether avoiding action needs and can be safely taken.

The OP would need to check on the council's highway fault reporting website to see if and when any such fault was reported, or on Fixmystreet (is that the correct name?) website, which apparently has a similar level of legal standing, as such info is supposedly pass on or viewed by council staff across the UK.