If they have intelligence on you, and you're signed up to a major ISP, they can use something known as "Lawful intercept" that's been around for quite a long time, (that was sufficient and not such a bad system in my view)
Basically, on the ISP's broadband gateway router in the exchange or data centre, they can identify your individual session - then copy and paste all of the data at the hardware level - going to and from your connection, into a tunnel - which terminates in GCHQ, where they get 100% of what's going in and out of your line.
I actually always thought this wasn't a bad system, it requires warrants to execute and seems legit, but done in the dark to both the end user and the ISP, the system is designed as such so that the ISP cannot find out or see who is being intercepted by "the man"