Perhaps. The quality of the Heraldry does not necessarily reflect on the quality of the porcelain. For example, perhaps you have something of an antique nature where the manufacturers made an unfortunate attempt to enhance their reputation.
The problem with that concept is that presumably they were attempting to enhance their reputation in a British market in which the clientele would recognize the unfortunate marshaling of the elements of the shield. Supporters, (the two lions), for example indicate nobility or a corporation. Obviously these arms are not a reference to a recognized title, and I really question that the College of Arms would allow such a grant to be made to a corporation. This means that, amongst the wealthier classes in older periods, the attempt would be counter-productive.
If the attempt was to enhance the manufacturer's reputation in North America they might have met with greater success. There, the wealthy often do not realize the simple principle that a coat-of-arms represents a single person, not a family and definitely not a surname. So, perhaps, the arms are a clue to the probability that the work was done outside of the United Kingdom but designed to suggest it was actually done there.
Adding terms such as 'Royal' (which in the British Commonwealth usually requires pretty specific licensing) might also be an attempt to suggest inaccurate origins. A clue in this case is the use of the Union Flag. This requires Royal assent, or permission from the King or Queen of England, directly. It is unlikely that such assent was ever given to a manufacturer of tea sets.
What may be significant here is not the validity of the armorial bearings but your own feelings about the tea set. If you really like it then that is good. Sometimes the simplest things, or stuff from the most humble origins have the greatest charm and can even be of the greatest quality.
Are there any other markings? Often place, manufacturer, sometimes designer are indicated. Do you have a provenance?
Simply commenting on the arms, a cursory examination strongly suggests a total lack of legitimacy. I feel that searching armorials, for example, would be a waste of time. I would hesitate to even attempt to blazon the arms as the colours are not really indicated. There are things missing, like the helmet upon which the crest (crown) is supposed to rest and the mantling which indicates the livery. The scroll at the bottom should have some sort of slogan or motto. The flags are reminiscent of the Cross of St. George (for England), but the bordure should not be included.
The style of shield and the way the lions are drawn is sort of late 18th early 19th Centuries, or more likely a later imitation of such styles attempting to evoke antiquity.
I think, basically, to anyone who has made a passing study of Heraldry, they would look at this and feel that it was just wrong. Someone unfamiliar with a human face would likely notice that they had a mouth, eyes, eyebrows, nose, etc.; but would be unconcerned if the eyebrows were under the mouth and the nose was up-side-down. The nose is definitely up-side-down here.
What I thought might be the White Horse of Hanover (in the upper right) could also be a unicorn in with a tressure flory-counter flory (a weird reference to Scotland.) That's what I mean by it being difficult to blazon. Blazoning is the verbal description according to formalized terminology. If you can blazon arms or a flag correctly you have a hope of searching for its origins. I simply do not have the skill to even attempt to blazon this. For example, I assume the cross in the centre is a Croix de St. Denis (blue cross on a silver field) but the fleur-de-lys' suggesting that are facing the wrong way. Looking at it more closely, the two on top are actually upside-down.
What really intrigues me is that the artist had some exposure to armorial bearings and certainly skill in rendering them. A little more thought and this could have been very impressive. It is almost as if they wanted to evoke the Royal Arms of England but avoid the difficulties that using them might have entailed. While some nations feel that it is quite correct to misappropriate any bearings they feel like, in Britain there still are legal barriers.
A forum specializing in porcelain may also have someone with some facility in Heraldry as well.