Honestly, the every British UK audio I hear for the word "sauce" sounds like "Saws" without pronouncing the S at the end as a "Z" sound. I wonder if it's a dialect?

I'm Bostonian (give or take), so I'm unaware of missing R's most of the time, but hyper-aware of them when I listen for them. British folks say "sauce" similar to how I would. Throwing that R in the trash.

The difference between standard pronunciation and conversational pronunciation is staggering. Factors for that include

• importance in the sentence. If you order tomato sauce with your pasta, the "sauce" part is rather unimportant as it can be inferred from standards.

• surrounding words. In a sentence, preceding and subsequent words (or part-of-words) can influence the pronunciation.

• vigilance. Tired speakers tend to slur their words more than usual.

• general talking speed. The faster the individual talks, the more corners they will cut with their pronunciation.

• Words are pronounced according to the speakers expectation of the conversational partner. You speak slower and more clearly to someone learning English as a second+ language than to your childhood buddy.

Word lists without context are much better for judging what people expect to hear when they anticipate the word. Here are some samples for the word sauce and horse. The 'r' in horse is pretty much silent in BE, but not in AE.

Source: I studied computational linguistics with a minor in phonetics.