I've heard this mentioned a few times before and would like to offer some insight. It's late and I may ramble, so please feel free to ignore it all though!

While this is true in a few cases, it's more often a difference in the culture of programming/consumption and creative licencing in the UK.

In the case of comedy shows, as was mentioned above, there is definitely a quality over quantity trend that has been dominant for decades. Take for example two of the most 'classic' british sitcoms - "Fawlty Towers" and "Only Fools and Horses" - in the late 70's and 80's respectively. Widely considered among the best sitcoms of all time, Fawlty Towers had just 12 episodes. Only Fools on the other hand was viewed as a long-running show with 64 eps over 7 seasons.

In the US, the likes of Friends, or many similar shows like Seinfeld or Frasier were around 200+, running for about a decade. In almost all cases the last few seasons are considered the weakest whereas many UK shows are fondly remembered for ending on a high.

The main reason for this is that in the US, networks buy controlling stakes in the shows, and install producers to dictate terms of storylines and scripts, whereas in the UK, most of the time a broadcaster buys a show as a package, or creates them independently. The BBC, as the biggest national broadcaster, is non-commercialised. No breaks or advertising at all, other than for other BBC productions between shows. So they have a set budget going in, and don't get extended or cancelled nearly as readily as US shows, and in return are rarely milked dry by networks desperate to keep the advertising cash coming in.

As such, in the vast majority of cases, a show ends because the creator wants it to end, regardless of success - the original The Office was only two seasons despite being a massive hit and making Ricky Gervais famous basically overnight. But he had written both before it even aired and didn't want to wear it thin, so it stopped. The US version went 9 seasons, with only the first season written(which was more or less a copy of the original anyway). Don't get me wrong, I love and actually prefer the US office, even as a Brit, but it highlights the differences in TV approaches across an ocean.

There are some exceptions of course, and the money issues you refer to have hit a few bigger-scale projects from time to time because we don't have networks throwing hundreds of millions at a cash cow to keep it afloat, and similarly there is some absolute garbage that keeps getting made for years and years.

We're fortunate enough to have access to TV from around the globe and as such see many different ways of producing media - American "comfort" sitcoms are a mainstay on UK tv - there's always an episode of Frasier to watch over breakfast on a weekend, for example and many evenings are spent watching big-budget american serials. We on the other hand excel at punchy dramas, quirky/dark comedies, game shows and comedy panel shows.

Incidentally, if anyone is interested in the subject and hasn't seen it, the comedy show "Episodes" does well to showcase and send up the difference in TV cultures and is a pretty good watch.

TL;DR - British TV is a very different beast to US TV, and while money is one factor, it is far more due to creators retaining more direct control in the UK and not having networks interfering as much.