A further meeting is likely to held next week to see if the draft clauses can be rescued.
The justice secretary had been planning to publish detailed draft clauses next week in line with a commitment in the Queen's Speech.
The draft clauses also contain detailed proposals for the powers of the second chamber as a revising body subordinate to the powers of the Commons.
Ministers are also looking at publishing draft clauses for a reformed House of Lords, with the aim of securing an all-party agreement before the next election.
Bradley said that the government would shortly publish draft clauses that would form the basis of new legislation early in the next parliament.
This will be followed by draft clauses on a proposed bill in the new year that will be formally introduced to parliament after the UK general election next May.
Indeed, between April and June 2009, the legislature injected cumbersome new language to the draft clauses involving the duties of communications providers, specifically toughening the onus on them to cooperate with official investigations and stop leaks from spreading.
But ministers say its draft clauses will not lead to the courts having to apportion "equal time" or "defining the nature" of parental relationship – both cited as reasons why the law failed in Australia.
Clegg has also promised that the internet tracking proposal will not be "rammed through parliament" and that open parliamentary hearings will be held to examine draft clauses of the legislation.
