In British usage, the government is strictly the executive. We don't have formal separation of powers, and the courts and Parliament are very clear they aren't part of the government. You can see this from Parliament's insistence on using 'parliament.uk' rather than .gov.uk, and the judges similarly with judiciary.uk.

Bluntly, Parliament is Parliament. (Her Majesty's) Government overlaps it, but is not the same. The DCMS committee in particular scrutinises government, but isn't part of it. I guess you could describe Parliament as being able to exercise (a few) State powers, but they really aren't a branch of government on the US theory.