R v Gul  UKSC 64
Quoting from the trial court, the judgement includes a jury question to the judge:
“Re: definition of terrorism in [section 1 of the 2000 Act], would the
use of force by Coalition forces be classed as terrorism?
The judge replied:
the use of force by Coalition forces is not terrorism. They do
enjoy combat immunity, they are ordered there by our government
and the American government, unless they commit crimes such as
torture or war crimes …
The Supreme Court noted that an ordinary language interpretation of the definition would include military activity, even if that activity is approved by the UK government.
As a matter of ordinary language, the definition would seem to cover any
violence or damage to property if it is carried out with a view to influencing a
government or IGO in order to advance a very wide range of causes. Thus, it
would appear to extend to military or quasi-military activity aimed at bringing
down a foreign government, even where that activity is approved (officially or
unofficially) by the UK government.
However, an ordinary language interpretation isn't the ending point of the analysis (as demonstrated by the judge's reply which uses the principle of combat immunity). The Supreme Court left open the possibility that international law could make the definition narrower than the ordinary language interpretation, but they don't get to that question in this case.
It is neither necessary nor appropriate to express any concluded view
whether the definition of “terrorism” goes that far, although it is not entirely easy to see why, at least in the absence of international law considerations, it does not.