Of our 4 kids, 3 were in the right year groups for going into the equivalent grade here when we moved, but my middle daughter had to move up a grade.
Her birthday is September, so she was just a few weeks past the cut-off date and when we moved here last year she should have gone into kinder but was already half way through P2 at home (home is Scotland - P2 is the equivalent of Y1 in England) and we managed to get the school here to put her into 1st grade instead. They are in a private school so did have to sit the WPPSI test and I suspect if she had struggled with that they may not have been so happy about moving her up a year. She is top of her class, even a year later though so I am so glad we got them to agree. Because her birthday is September she is only a little younger than some of the other kids in the class and it's really not been noticeable. To be honest though - the biggest and most noticeable differences are the cultural things rather than the age and we have found that with both of our older ones - less so with the youngest two who are in Pre-K.
What we have found academically is that the kids start off slower than they do at home in Scotland, so kindergarten is a lower level than P1 would be. (I don't know how Reception compares to P1 in Scotland so can't compare with the English system) There will always be kids here, for instance, who finish kinder not able to read properly (even in a private school) and that's totally OK here - 1st Grade is where it really heats up for them and even then, that is less pushy than P2 at home! We found a big jump between 1st and 2nd grade this year. 1st grade they were expected to learn, but they were still treated very much as wee ones, 2nd grade the level of expectation in terms of work and responsibility, is much higher. My eldest is 4th grade now and I would say the level of work is pretty much on a par with what he would have been doing at home this year, so I think 2nd and 3rd grade are really where they push it.
All of our expat friends have found the same as us (both those in private schools and those in state) - that the literacy stuff is generally behind the UK here, but the maths side of things is pushed further, quicker. My son was top of his class in a very academic state school back home, but was behind in maths when he arrived here. He's caught up now, but he's had to work hard on it because he missed key things that his class learned before he arrived.
The other big difference is the testing - it maybe isn't so bad in kinder, but it definitely hots up in 1st grade - they test for EVERYTHING here and get a grade for everything! Some schools (state and private) give the kids daily conduct grades, and you get some form of report card every 4.5 weeks - a full report card every 9 weeks and a mid-way progress report in between! That is very different to home for us and it's been interesting to see my kids respond to that.