The United Kingdom’s Supreme Court has a YouTube channel (“UKSupremeCourt“) which includes video recordings of judgments.
There is also this very clear introduction to the Court, ostensibly designed for students, but in my opinion a useful overview for everybody else too:
You can also watch Supreme Court hearings live on Sky News: http://news.sky.com/info/supreme-court
The schedule of cases to be heard can be found on the Court website: http://www.supremecourt.gov.uk/current-cases/index.html
Readers of this blog might be particularly interested in the Alexandros T cases (hearing date 8 July), involving an insurance claim and proceedings in different jurisdictions, on whether the UK’s Court of Appeal was right to stay proceedings in relation to Council Regulation (EC) No 44/2001 of 22 December 2000 on jurisdiction and the recognition and enforcement of judgments in civil and commercial matters.
You might also be interested in this previous post on UK legislation online.