Under BPI proposals, ISPs would be expected to monitor the activity of illegal downloaders using a 'three strikes and out' rule. This would start with written warnings being issued to offenders, and ultimately lead to the suspension of internet access for illegal downloaders who ignore the warnings.
But Dunstone said in a statement the demands were unreasonable and unworkable. He added that it is not his job to be an internet policeman.
"We do not control the internet nor do we control what our users do on the internet," he said.
"We believe that a fundamental part of our role as an ISP is to protect the rights of our users to use the internet as they choose. We will fight any challenge to the sanctity of this relationship with every legal option available to us," he added.
Dunstone's comments follow rumours that Virgin Media will be the first ISP to target illegal music file sharers. However, according to Digital Spy, Virgin Media has since denied taking part in a pilot scheme.
"We have not agreed to the three strikes scheme, not started trials with the BPI or any other rights holder, and not decided to snoop on customers and inspect their data," a Virgin Media spokesman said.
Chief executive of the BPI, Geoff Taylor also denied any agreement with Virgin Media had been reached.
"Unfortunately it simply isn't true that we have agreed a pilot - or any sort of deal - with Virgin Media, though we continue to work towards that. We think that every socially responsible ISP should help their customers avoid the illegal use of their broadband account," he said in a statement.