The main body of the article is pretty incoherent and rambling; it never really clearly states what the law is actually about.
If you actually go read the linked BBC article[0], you'll find that what's happening is somewhat less alarming than the article would lead you to believe. From what I gather, a politician is attempting to increase the maximum sentence of an existing law from 10 to 15 years, and to apply it to streaming content rather than just downloaded content.
There are definitely free speech implications and concerns here, but it's not nearly as dire as the article would imply.
[0] https://www.bbc.com/news/amp/uk-41479620
*Also, the subtext of the BBC article > People who repeatedly view terrorist content online will face up to 15 years in prison, the home secretary has told the Conservative Party conference.