Is Umbridge a commentary on British government's educational policy?

[Carol]

I raised a couple of questions about Umbridge on the main list that I
hoped someone would respond to here, but not a peep. What I'd like to
know is whether British readers think that Umbridge is a caricature of
Margaret Thatcher (whom JKR evidently didn't like). I'd also like to
know whether Hermione's remark, "It means the Ministry is ("are," if
you'r British) interfering at Hogwarts," has any bearing on government
interference in British schools, "public" or otherwise.

As an American, I read the line and think about government-sponsored
programs like "No child left behind" (which many people think are just
"throwing money at the problem" and tying teachers' hands), but I have
no idea whether anything comparable is happening in Britain that JKR
might be criticizing.

BTW, I understand that JKR is criticizing corruption and bureaucracy.
That's not what I'm asking. I'm wondering whether Umbridge (in OoP,
not DH) has any specific relevance to British politics or educational
policy in the Thatcher era or later.

I take the (male) Prime Minister in "The Other Minister" to be simply
a mild satire on self-interested politicians. Umbridge is obviously a
much more sinister figure.

Carol, isolated from British thought and politics in the world's most
arid backwater