Yes you can. In the UK people sue the government, or specially the NHS, over treatment decisions all the time. Including over things like denied coverage of specific drugs etc. (usually when there's no proven benefit from a given drug).
And as I pointed out: If you think they are too strict, then you can pay for a private insurer to cover things the NHS doesn't cover or won't do fast enough for you.
In Hillary Clinton's proposed health care plan in 1993, no, you weren't allowed to sue. You could get an appeal from a Board, but that's it. The proposed legislation explicitly said there could be no other review.
Note that this is a very good cost containment strategy. Note also that this can probably not reduce patient outcomes at all. Note also that it is extremely unpopular.
And as I pointed out: If you think they are too strict, then you can pay for a private insurer to cover things the NHS doesn't cover or won't do fast enough for you.