The bulk of primary school admissions in England are done for entry into Reception (age 4). Entry into another year group will depend on how full the class/es are in each school for that year group already. Unlike other places (Scotland, US?) you can’t just decide where you’d like your child to go to school, move nearby and get a school place. You need to find out where the school places are, by speaking to the local authority education services.,
The City of Kingston upon Hull is surrounded by the East Riding of Yorkshire. I don’t know Hull very well, in the past it has been very run down in parts, but has picked up a lot in the last few years.
I am much more familiar with the East Riding. Villages and small towns around Hessle, Anlaby, Cottingham and Willerby are all perfectly commutable to Hull, if you fancy looking further afield. I know a few families in North Newbald and South Cave too. Wherever you go, check out flood risk first!
In your position, i’d be tempted to look at Berverley, although traffic to Hull is busy at rush hour - may not be a problem if you work shifts?
I am afraid I don’t know either East Riding or Hull well enough to comment on how you would be welcomed as a dark-skinned family. Hull has a big university and big docks, so there is a long history of overseas visitors to the area.