I suspect it is an open sugar bowl. That's how it was described on a site in the U.K. for the same pattern, but in its smooth (instead of scalloped) interpretation. My first impulse was to say tea bowl, but that would have been so affectatious, since it's obvious this pattern is much, much later than when tea bowls were mainstream. There is a lot of English garden around and it's 20th century. My second reaction was a buillon cup, and I suppose that's possible. It's just a lovely pattern.

The cup with no handle is a "slop bowl"....also called a waste bowl. Such a piece was usually included with tea sets of the era. It was used to pour cold tea from a cup when you wanted a refill. Almost always found in a silver tea set, less often in a china one....perhaps because they had many uses and got broken.

Here is a link that might be useful: slop bowls

Was hoping you'd chime in on this one, as occidental tea sets are not exactly up my alley. So, since in that era, tea was simmered from leaves and bags not used, what was a 'slop' bowl used for?

Slop bowls were used for "slop"! LOL! When using a hot water kettle and tea concentrate, you warm the cup with a bit of hot water from the kettle pour it into the slop bowl then put in your tea and more hot water. When you come back fro a refill, you dump the dregs of your cup into the slop bowl (or rather the server does) and refill your cup as before.
And tea is never simmered, but rather steeped.

I learned a lot of things in college....in addition to experimental psycology, qualative chemical analysis, French restoration drama, modern American literature, the history of art with the great masters....I learned how to make and serve tea...Every Friday afternoon, tea was served by the house mother in every dorm. The students trooped in like lemmings to chat, have a cup of tea and to snack on little sandwiches and brownies, while Mrs. Wassername poured tea.
Oh yes and I learned how to drink beer in college too!! LOL!

The antique china slop bowls that I've seen (I own one) are considerably larger than the little one shown above. If the Coalport is the size of the one I have in Mason's Manchu it's comparable to a Chinese tea cup & wouldn't hold much waste. I've seen them called sugar pots although with a saucer, bouillon seems more likely.

Thanks everyone ... I had wondered about it being a "slop" bowl since I have an old family tea set that was my great-great grandmother's (Chelsea Ware - Bronze Grape pattern, approx. 98 pieces) and there are slop bowls in that set, but they are larger and much different than the tea cups ...

This cup with no handle is exactly the same size as the tea cup ...

calliope - you said there is plenty of this pattern around, but I'm not finding many pieces that have this scalloped edge. Replacements has only a few pieces, and there are only a few on eBay ... where are you finding this pattern?

My neighbor is wondering if there's any value in the pieces ...

I had a lot of hits on it when I checked the pattern, but a good many of them were 'asides' like on thimble sites, and also a good many were in the U.K. You are right in that the design is more prevalent in the plain pattern and not so much in the scalloped, and the scalloped is so much more dainty to me. Of course there is value in that collection, but I can't help you in evaluation. I am not familiar with Coalport, but know it's collectable.

I would assume it is a lidless sugar bowl and that it doesn't really belong on the saucer. I have several English tea sets and all of them have that lidless sugar bowl -- about the same size was the tea cup.