The lower amounts of financing limit the budgets on the series - While certain series (like Doctor Who and Bodyguard) have large enough budgets to make them look like US-based programs, most do not and they have a “cheap” look to them if you have watched television for a number of years.
Those lower budgets won’t allow the series to attract top name North American actors - American series can attract a range of actors from around the world. It’s rare, however, to see actors from outside the Commonwealth and certainly few of those who are working often in Hollywood on British television (https://www.quora.com/What-is-the-weakness-of-British-television).
Their limited budgets and runs make second run syndication nearly pointless - Fawlty Towers has 12 episodes, Yes Minister/Yes Prime Minister has a total of 53 episodes, and the IT Crowd has 17 episodes in total. While that makes it easy to air in the UK and the Commonwealth, it makes it unlikely to be sold in North America, the most lucrative syndication market. If the British episode model changed, it’s likely that American production companies would enter the market and there would likely be higher budget programs created.

I do not think "Keeping Up Appearances" looks cheap. I thought they did a great job as they were going on location all the time. Now the original "Are You Being Served" is a different story.