"The new Bill must close all the old loopholes, and the new overly-broad powers that are in the current draft of the Bill must be eliminated if we are to avoid repeating this scandal of the Executive writing its own powers."
That's an overly-broad statement. We need more specific requirements. Here's my suggestion.
1. The presumption of innocence is an important principle in English law. A corollary of that is that, whilst an investigator will necessarily regard individuals as suspects prior to conviction, the population as a whole must not be treated as suspects. Mass surveillance is not an unacceptable means of investigation.
2. Any interception must require a warrant.
3. It is unacceptable that a warrant be granted by a politician or by an official of the investigating body. It must be granted by a judge or magistrate.
4. There must be a regulatory oversight of the process over and above that provided by the independent granting of warrants
5. The regulatory oversight should review the outcomes of intercepts. The percentage of significant outcomes should be compared against the sources of requests for warrants and against the granters of warrants. In the first case this would be to check for attempts to slip unjustified, overbroad requests through the system and in the second to check for regulatory capture. Suitable action should be taken in the event of the discovery of anomalies including withdrawal of the ability to make requests or to grant warrants. There should also be spot checks on the returns made for this statistical review.
6. The regulator should also respond to complaints from members of the public in regard to abuse of the interception powers.
7. The regulator should have the power to act when abuses are discovered. Available actions should include requiring agencies to take disciplinary action, criminal proceedings and ordering public apologies and compensation to victims of such abuse.
8. The regulator should publish regular reports including summaries of the statistical reporting, complaints and all actions taken in the event of abuse.
If the regulator needs a motto "Quis custodiet ipsos custodes?" seems appropriate.