Well, one of the obvious problems is: how do the Indian colonists get to Europe?
I mean, it's not like as if there's an easy way to Europe from the Indian Ocean, even if the old "proto-Suez" canal could be used by the Indians (which is not going to be likely if there is a strong Caliphate effectively blocking this route), and the only alternative route is rounding Africa, which is an awfully long way to travel to colonize a place that has very few desirable resources that can be obtained more easily in other places...
And even if you would remove Islam or keep it fairly insignificant (according to tradition, Mohammed didn't start preaching until about 610 AD, so a POD to prevent the rise of Islam would still be possible), then that still leaves the fairly strong kingdom of Axum in control of the crucial Red Sea route towards Europe.
But nonetheless, some (perhaps dynastic) alliance between an Indian maritime power and Axum could be possible (which would be an interesting scenario, by the way), and the Indians and the Axumites could then establish a few colonies along the Red Sea coast, and due to the results of the last great Byzantine-Persian War, even Byzantine Egypt could be weak enough to allow the Indians and Axumites to effectively take control of the "proto-Suez" canal.
Now I know that especially that last part is not all that likely, since the Byzantine Empire still had a powerful navy in the Mediterranean, making it unlikely for even a combined Indian/Axumite force to take full control of the whole route. (after all, what use is a route that connects the Red Sea to the Mediterranean if the Mediterranean part of the route is blocked off by the Byzantine Navy?)
Only if there is some sort of treaty between the Byzantines and the Indian/Axumite alliance about using this canal would it be likely that the Byzantines would just let them use this route.
That - or the route becomes available because the Byzantines lose Egypt alltogether, and the scenario of Axumite and Indian colonists taking all of Byzantine Egypt is, least to say, not all that likely...
In fact, if the Arabs aren't gonna take Egypt (which is not very likely without a strong unifying force like Islam), then the only other nation that would actually have a chance of successfully invading and taking Egypt at this point, would be the neighbouring Christian Nubian kingdom of Makuria.
In OTL, Makuria actually managed to resist the Arab invasion and lasted until about the 14th century, so it may just be strong enough to invade Byzantine Egypt, which was not only severely weakened by the Byzantine-Persian War, but its Coptic population also suffered severely from religious persecution.
And if, during that invasion, the Axumites and Indians ally themselves with Makuria, then it would be likely that the Axumites and Indians either take full control of this "proto-Suez" canal, or can at least use it with little or no restrictions.
..
Allright, now we've gotten the Indians (and Axumites) in the Mediterranean...
Now suppose that they can just trade relatively freely in the Mediterranean (which is still largely controlled by the Byzantine Empire; it controls Cyrenaica, southern Italy, Byzantine Africa and most islands of the Mediterranean and the Empire still has a formidable navy), in order to get to Britain, they'll have to pass the Strait of Gibraltar first.
Now this might just be relatively easy (provided the Byzantine Empire doesn't interfere), because the Visigothic kingdom in Spain is crumbling during the 7th and 8th century, so there actually is a good opportunity to establish some colonies at strategical positions, including at Gibraltar itself, which would give the Indian/Axumite allies full control of this route.
Now then, these colonies, of which some would be on inaccessible parts of the southern Spanish coast and some others on the Northwest African coast, would be fairly independant from the Indian and Axumite homeland, and they would mainly live off local trade.
...and Britain indeed has some natural resources, like chalk, slate, limestone, and tin, which ninebucks has already mentioned, so Indian merciants based in these colonies around Gibraltar would indeed have a good reason to visit Britain.
And it just so happens to be that Britain wasn't quite united at this point, not to mention the fact that at this point, Britain itself was divided into warring Celtic and Saxon kingdoms.
At first, the Indian merciants could establish a few settlements and outposts on the British coast, trading and interacting with the local British and Saxons.
The next development is that these colonies could become relatively large and powerful city-states, which start to influence the neighbouring kingdoms. (note that in this scenario, the Indian/Axumite colonies around Gibraltar and on the British Isles are still one state)
And ultimately, these Indian colonies could start absorbing some smaller local kingdoms, and grow into a well-organized empire, which then conquers or just absorbs the remaining Celtic and Saxon states.
And after that, this empire could even expand towards Ireland and Scotland.
...and as long as the ruling classes and dominant culture remain Indian, we now have an Indian-ruled Britain.