I know in modern Britspeak one would say, e.g., "the government have ordered..."

I wouldn't say that. Generally speaking I'd think of the government as a singular entity despite the clear differences between many of its members.

"The Labour Government has increased taxation exactly as predicted"

"The Government has failed to achieve unanimity on this issue"

Nope, I can't think of a time when I would treat government as a plural, though I can imagine that it may make sense in certain contexts. Incidentally I can never imagine Parliament being treated as a plural.