There isn't a UK education system.
Scotland has a different education system, exams taken are different and so are ages for going to high school and to uni.
Many primary schools in Wales teach in Welsh - do you want your children to be bilingual?
From this point onwards I'm talking about England.
By law all state schools have to have a daily act of worship that is broadly Christian. Schools can ask for an exemption but it is usually Jewish or Muslim schools who, understandably, ask for this.
Many schools, particularly at high school level, ignore the rules. Some will say a prayer before lunch that is basically 'thank you for the food God'.
At the other end of the scale the RC schools might pray 3 times a day, have mass once a week, teach RE every day and relate other lessons to RC 'values'.
Again by law children have to learn about at least one other faith, this can vary a lot in the teaching. Some schools teach about all faiths, some only teach about one other.
You don't say your children's ages but in an RC school they would be expected to prepare for first communion and confirmation. Would you be happy with that? If not and your child was the only one not preparing would they be happy?
How long are you intending to stay in the UK? Is it a permanent move? What do you want from high school?
Parts of England have the 'grammar system' - basically children sit an exam at age 11 and if they pass go to a grammar school, those that don't go to a secondary modern or a comprehensive. Comprehensives take children of all abilities, but in an area with grammar schools they obviously take the ones who didn't pass the test.
Some areas do not have any grammar schools, all children go to comprehensives and yet more areas have a mixture of grammar and comps. Birmingham has grammar schools as well as comprehensive schools but not all children take the 11 plus exam and some of those attending grammar schools are bussed in from other areas.
Some high schools have specific feeder schools so children for the feeder are almost guaranteed a place in the specific school while children from other schools are not.
Feeders are not always close to the high school. I went to an RC school, since leaving it has merged with another RC school. It has feeder schools who are given priority in the admissions process. One of the feeder schools is in another town that doesn't have an RC high school, this means children 8 miles from the school have priority over a child living in the same street as the school but attending a non feeder primary.