Googling some of the 1990s Channel 4 titles on the site The Telefantasy List (page seems to be down but there's an archived version here), I think I've found it--there was a documentary series called Equinox which had some one-off films called "Equinox Specials" including The King of Chaos from 1998, which has the following synopsis:
Docu-drama of what the media might be like by the year 2012. EQUINOX's
first drama, set in the future, focuses on the facts behind the
suspicious death of media mogul, Liam Keller, whose software
applications have had a huge impact upon broadcast TV, earning him
enemies around the world. In the late 1990s, Keller had devised
`Gambit', a virus which enabled all technologies (the internet,
television broadcasting, e-mail) to converge - to communicate with one
another. Found floating in the Thames, a television current affairs
programme sets out to explore how Keller might have met his death.
Through Keller's life story this drama explores the consequences of
future technology, reflecting on what might happen to our present day
media over the next few years. The programme also includes interviews
with leading futurologists, including British Telecom's Director of
Research Peter Cochrane.
The telefantasy list also notes that "'The King of Chaos was repeated on Channel 4 as an episode of Futurecast in 2000", and looking up "Futurecast" I found a summary here which lists some other episodes that seem to match what you remember:
Futurecast, first aired on Channel 4, April 2000, is a trilogy of
sci-fi dramas set in 2012-13. Each episode - "The Kidnap", "The King
of Chaos" and "Newborn" - deals with the consequences of technological
and scientific advances. "The Kidnap", directed by Bryn Higgins, is
about a couple, Louise and Craig Richardson (Paula O'Grady and Gary
Sefton), who hire radical healthcare activist, Sepp Kurtz (Adrian
Shiller) to hack into the world's most popular news channel to
broadcast the trial of a powerful biotechnology boss, Terence Singh
(Ranjit Krishnamma), they kidnapped to get the gene therapy needed for
Craig's leukaemia. "The King of Chaos" deals with a murdered software
mogul, Liam Keller (Danny Webb), who may have created the world's
first intelligent software. Who killed him and what were their
motives? "Newborn" is concerned with how people react when the
internet becomes intelligent. A decision is made to shut it down, but
with what consequences? How will this affect the flow of information?
"Newborn" sounds like the one you were talking about with the viral A.I. I couldn't find a version online or on DVD, but the company that made Futurecast, Stone City Films, has a page with a short clip of the episode "The Kidnap" here. (update: the Stone City Films page is down but you can see an archived version of the text from the page on archive.org here, and the clip from "The Kidnap" is available on vimeo here, although the first 10 seconds have some kind of audio stutter problem).