Bit of a no-brainer really
I'm sure the vast majority of people would agree that the police should be able to investigate crimes, or (strongly) suspected crimes, and that, in the case of serious crimes (which needs to be clearly defined), would include asking a judge to give them the authority to access various records relating to the activities of known or suspected criminals. So far, so obvious.
Whether people agree that unaccountable 'Security Services' should have any role in domestic law enforcement is another matter.
The job of the police is to investigate crime and criminals, all crimes, including those committed by MI5, therefore they need data about criminals. They have absolutely no need to gather or access data relating to people who are not serious criminals.
It may not be easy for them to work out how to differentiate, but given their general success with addressing serious crime already without draconian data trawling, I would suggest that they have more than adequete data available now, without the need to make us pay for our own surveillance through higher ISP costs.
Serious crims will always find a way to avoid surveillance (El Reg commentards have already suggested many possible options) so only the law-abiding will have their communications tapped. So why bother?
Dear Mrs May, I am not a serious criminal so kindly fec off!