What evidence is there of Asians and Africans in medieval Britain other than Moors in the 7th century?

As for Asia, I have heard about the connections between Anglo-Saxon England and certain countries of Asia. There is even proof about it when garnets from as far as Sri Lanka and India were found in the burials of the Sutton Hoo ship dating back to the Anglo-Saxon period here. However, I am not sure of how the garnets even got there. Many people wondering about this generally assume that those garnets, although made in Sri Lanka/India, were passed through several hands on it's way to England.

I have tried to research hard on how the garnets even came to England but then I stumbled across a PDF here which could explain it.

...the journey must have commenced along the ancient maritime trade routes of the Indian Ocean, sometimes referred to as the Maritime Silk Road and continued from there, by ship along either the Red Sea to Coptic Egypt (at that time under the control of the Byzantine Empire) or via the Persian Gulf to lands controlled by the Sassanid Empire (it has been suggested that at least some garnets found in Kent may have passed through Sassanid workshops: Jo Ahmet pers. comm.). Either way, the garnets most likely passed into the hands of the Byzantine elite, and from there reached the Merovingian elite, perhaps via riverine travel along the Danube and the Rhine. Kent’s close relationship with the Merovingians meant that it was in a favoured position to receive both finished objects bearing garnet-inlays as well as loose garnets (whether raw or worked) with which to adorn locally produced prestige items.

Though, it doesn't end here:

Probably. But we should not under-estimate the capacity of individuals to make very long-distance journeys in the past. The inhabitants of early medieval Europe certainly had heard of India (and probably also of Sri Lanka, ‘the land of gems’). There was believed to be a Christian community, centred around a shrine dedicated to St Thomas, in southern India, and the Frankish sixth century chronicler, Gregory of Tours, was able to describe the shrine since he knew a monk who claimed to have travelled there. Later, the Anglo-Saxon Chronicle records that in the year AD 833, King Alfred the Great despatched Sigehelm and Æthelstan to carry alms first to Rome, but then to the shrines of St Thomas and St Bartholomew in India, though it is not known whether they succeeded in this journey (see https://www. caitlingreen.org/2019/04/king-alfred-and-india.html for a discussion of this embassy). So, we should not completely rule out the possibility that someone may have travelled all the way from sixth-century Kent to Sri Lanka, or vice versa. And certainly, the latest (and ongoing) genetic studies have revealed at least one individual with non-European ancestry buried in seventh-century Kent, further demonstrating that long-distance travel was not unknown.

I'm not sure if that person buried in Kent dating back to the Anglo-saxon period is a Sri Lankan who brought these garnets or probably someone else. That's all what It said.

It should be noted that Sri Lanka was even known to the Anglo-Saxons as 'Tabrobanen'. There is proof on this map which could date back to the Anglo-Saxon period, probably 1040 or before. Its called the 'Anglo-Saxon Cotton World Map':
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This map depicts Britain in the west (bottom) and Sri Lanka or 'Tabrobanen' in the east (top), in fact Sri Lanka was the most distant land to the Anglo-Saxons at that time.

I still unsure that there could have been people as far as Sri Lanka in the Anglo-Saxon period. Maybe these sources can indicate but I haven't seen anything as far as that.

I'm mainly talking about the Asians here, btw.

Potentially Chinese skeletons in London have been dated from the 2nd to 4th century. I have only seen vague explanations for their presence. Some methodological concerns were also raised about these findings.

The Kingdom of Makuria (Nubian peoples, think south of Egypt) was a Christian kingdom and I would suggest that is the likely homeland for Black people who made it into medieval Europe. It's heavily neglected (crusaders and Christianity tends to be portrayed solely as 'white', but that is heavily incorrect as three Christian kingdoms existed to the south of Egypt). You can find their Makurian presence in crusades, and this was a likely link back to France and England.

From the 4th crusade comes a an account in Constantinople where the crusaders come across a Nubian man

And while the barons were there at the palace, a king came there whose skin was all black, and he had a cross in the middle of his forehead that had been made with a hot iron. This king was living in a very rich abbey in the city, in which the former emperor Alexios had commanded that he should be lodged and of which he was to be lord and owner as long as he wanted to stay there.

The king mentioned above was on his own pilgrimage...From his homelands to Jerusalem, to Constantinople, then Rome, and finally Santiago de Compostela (far north west of Spain).

The shrine to St. James at Santiago de Compostela in northwest Spain dates to the 9th century. The Camino de Santiago (Way of St. James) was (and remains) one of the most popular pilgrimage routes in medieval Europe.

Medieval Spain was a well-known multicultural melting pot of peoples. Pilgrimage to Santiago is mostly associated with European Christians, but this is an incorrect assumption. In fact, one 12th century Latin text lists Nubians as one of the 72 different nations from which pilgrims came to visit the shrine. Even more, a century after King Moses George’s trip, in 1312, historian Ibn ‘Idhāri al-Marrakuši also mentioned Nubians as pilgrims to Santiago. So even if the king did not go—or did not survive the trip—other Africans appear to have done so, and be counted among the black faces present in medieval Europe.

I believe from here, a few of these people made their way through Europe and are likely the source of those mentioned in James IV of Scotland court. Oddly, the link suggests that we know more of these people from the Christian Mukuria Kingdom than we do of them in Roman society.

I have a few sources, but https://www.publicmedievalist.com/uncovering-african/ seems best (quotes above taken from here)