Under the current RIPA rules if the government or a security service wanted to "tap" your connection (i.e. collect some very basic logs of your online server times/dates/accesses - BUT NOT THE CONTENT OF YOUR COMMUNICATION) then they'd first need to seek permission and only then would the ISP be required to take some action.
Meanwhile the new Comms Data Bill intends to go a lot further but it's currently being rewritten after significant opposition and a scathing review.