Especially since it comes up again in a later episode, with Humphrey discussing the ramifications of civil servants conceding the reigns of power to ministers who'd be under pressure to carry out voter demands.
Humphrey: "How would you feel if Radio 1 played pop music 24 hours a day? Or if they took the culture programmes off of television?"
B responds "I don't know, I never watch them"
Humphrey says "Well neither do I, but it's vital to know that they're there!"
While it was satire, the was a lot in it that could very well have been reality.
My primary criticism is that it didn't actually satirise the government's ideology or policies -- the main criticism was of politicans, civil servants, and interest groups like unions. These were actually in line with Thatcher's ideals and policies at the time (it's therefore unsurprising she said it was her favourite show).
I'm not trying to blunt any of their wit, just point out that (like most works) it had its shortcomings. It's unlikely the BBC would've aired it if it had just been a scathing ridicule of the PM at the time.
The workers (and thus the unions) were opposing government policies that were hurting them. Funnily enough (though unsurprisingly), strike rates as well as union membership fell under Thatcher because of her union reforms (which removed much of their bargaining power) -- and so the commonly held view of daily strikes in the 1980s (something Yes Minister capitalises on) isn't really an accurate portrayal.
By laying criticism on one and not the other, Yes Minister showed their Thatcher bias. And it's not at all a stretch to say they had a Thatcher bias -- Thatcher herself said that Yes Minister was her favourite show. So while Yes Minister was very heavily critical of the civil service, they weren't fundamentally critical of the views of the government. Thatcher was very strong on civil service reform too.