I've worked in a village school. Granted not as small as the one you mention. Our PAN was 25, so 1 class per year group (with most classes having about 22-24 children).
A huge positive for me was the community feel. All staff knew every child in the school. Likewise the children all knew each other and the older ones really looked out for the younger ones. We went on whole school trips, where younger children were buddied with an older one. In fact, we used the buddy system on a day to day basic. They'd have weekly buddied reading time etc. I loved my time there and enjoyed whole school events such as the Christmas play, Harvest Festival, Summer Fete etc, as staff also got to know all the parents. It was like one big family.
However, there is no getting away from the fact that friendship groups are often limited. They literally go up with the same 15-20ish children throughout the whole of their schooling. It's great if they all generally get on, but if you have any children who clash it can make life tough as you can't just split them up the following year in different classes, like you can in a 2+ form entry school.
We also use to find that the children sometimes found the move to secondary more daunting, as they've only ever known the same small pool of classmates since Reception. As lovely as the family/community feel of a small village school can be, it can be a massive culture shock when they go up to secondary with hundreds of kids they don't know, often from vastly different backgrounds.
I currently work in a 3 form entry school in a large town. I really miss being on first name terms with every single child in the school, but I do think our children are generally better prepared for the transition to secondary as they're more use to having a bigger social network. They're use to changing classmates each year. Whilst the 90 kids in each year group do get to know each other quite well by the end of Year 6, they're use to chopping and changing within the year group in terms of who is in their class, who is their best friend at that moment in time. It's not quite as intense as the close nit friendships of a village school cohort of 20. Children in bigger schools do tend to find it easier to form new friendships in secondary, simply through having a lot more practice. Each September they have to put in the ground work once again to establish friendships within the class. The dynamics change each year with a slightly different mix of kids. Whilst I totally understand that some parents prefer a village school for their kids so they don't have to work on friendships every single year, ultimately I think they get out of practice by the end of Year 6. For some of them, it's been years since they've met new children to befriend. Then suddenly they go up to secondary, their primary best friend goes off with someone else, and they have no idea how to reach out to others and form new friendships.
I'm speaking generally of course, as all children are different, but I have noticed a pattern between the two very different schools I've worked at in terms of how adaptive the children can be when it comes to making new friends.
You can always help the socialisation aspect by getting them involved in clubs out of school, maybe back in the town you're moving from if you drive? Especially if the secondary school they're likely to attend is in the town. Scouts/Guides, swimming, dance, gymnastics, football, parkrun, music lessons etc, whatever they're interested in. If they have friends out of school too, they're more likely to cope better mixing with different children when they eventually leave the comfort of their village primary.