Unless I missed a bit that said this takes place in one of a handful of countries that don't use a "first academic day of the school year is sometime last half third of the year", or more accurately the small number that have the first day in January, therefore being either Malaysia, Singapore, New Zealand or Papa New Guinea. These are the only ones listed on the 'first day of school' wikipage, with a handful mentioning february at the start, with Australi being a 'maybe sometimes if the regional gov decide' kind of thing. common theme being - northern hemisphere, between June/July to October. southern hemisphere, well any time of the year really. Japan is April, Vietnam is September and Kora is March. It's... muddled.
But the first day of school for the UK is generally in the first and sometimes the second week of September.
why is this important?
For the sake of 'we're twelve months apart but one of us was born in x month and the other in y month, so we're in the same year of school', it relies strongly on the cut-off point for school-age. i.e. In the UK, Infants school is Reception, Year 1 and Year 2, Junior School is Year 3, 4, 5 and 6. High School is Year 7, 8, 9, 10 and 11, and then Sixth Form is basically college-level stuff but you stay at your high school, or you go to college. (where it gets confusing as to whether or not it's university, as both words are used interchangably in parts, and some places college is to university as junior is to high school... aka the previous step and not the same damn thing.) Now, "High school age" in the UK (for year 7), is eleven years old. As in, far as I know, if your birthday is in September? then like Hermione, you turn Twelve not long after going to Ho- Um, After starting high school. Good luck if it's so early in September that technically you might already be twelve on your first day (say, the 3rd, and the first day of school that year lies on say, the 5th.)
However, lets say you were born on the 1st of september. Say... three am. And you're a twin. The younger twin. And your older twin was born six hours before or something. First, your mother has my sympathies, but, second, that means he or she has a DoB that is 31st of August. And that means they're actually in a different year from you... and also, the youngest of their class, whereas you (DoB 1st September) are the oldest of the next class. So here, the cut-off point is the midnight between the 31st/1st of September.
For a school that has an Early-year start, they might get away better with sticking to new years. So. Either the MC (is he the older?) was born January, and Lauren born in in December of the same calendar year (or swap the names I haven't played past where I learn about their age difference)..
Which presents a point that would have been good to make in the story, given the mention of the born and raised in Birmingham in the UK yet the other mention of the dad's job causing them to move with change of schools and loss of friends... the move was abroad, and the different school year involved caused them to go from being in different classes to the same class.
I don't know if the term 'Grade' is used anywhere out of the US, and I know it's not one in use in the UK, so the 'moved abroad' is a given at this point for me.