I think you are right that with very small populations like Travellers, a lot is to do with the small population. And there is a desire to keep culture and traditions, and if we are being honest, marrying outside would very likely dilute those things in the case of a group with such a different way of life.
Some social anthropologists think that is the reason that Jews at certain times in their history, for example, had so many complicated rules for remaining kosher. It makes it quite difficult to fully integrate into the general population, you can't really live together that easily, and intermarriage would be much less likely. So they continue as a distinct and separate population. And there is much less chance of dilution of religious observance then as well.
I think we should probably be honest that for groups like this, they are in many ways being asked to give up parts of a distinct way of life, and that will feel like losing their culture. And that is a hard thing in your own country.
The situation with immigrant communities is a little differernt. With small numbers coming into a large, established community, a family of newcomers will by necessity have a lot to do with the people around them. It will be natural to adapt in many ways to what people do around you, and certainly children born there are likely to do so. Such newcomers are often also, in such cases, disposed to do so - they know when coming to a new place they will have a new culture to adapt to.
And then there is the economic element - the fact that once you come to the UK, a lot of the economic drives toward things like cousin marriages are not there. That should make them less desirable over time.
Of course, the more similar the basic values and traditions people share, the simpler this process is likely to be. I think this even extends to religion to a large extent, a shared religion is another place where people can spend time together or can relate customs, holidays, and so on. It's a point of connection that draws people together.
The more differences, the more change is required, and the fewer connections, and the more effort is required on the part of the community to integrate new people. And it is far more difficult if there are a lot of them, and there isn't so much need for them to interact with the surrounding community. Especially on a social and friendship basis (rather than at work for example.) Especially where there is not a shared religion or belief system, pressure to change under these circumstances seem more like pressure on religious identity which is often resented.