I'd pay up if you want it to stop.
However, you have broken all the rules of natural justice by contacting these people and believing their threats. If you did make an error and believe they are owed the money, by all means - pay them what they say you owe - and move on. You'll enjoy the preace and quiet this will bring.
If, however, you are like the rest of us and view this as extortion by mail - welcome to the club. STOP communicating, and file carefully (this does NOT mean 'BIN') all the incoming letters begging you to pay. The only thing you have any requirement to answer is a court summons, and in the unlikely event of you ever recieving this, you can challenge them on many, MANY levels - but they won't waste their money on such action - it easts into their profits!
Don't be bullied - but if you cannot cope, pay up. There's little point making yourself ill if you do not have the resolve to laugh at their antics.