Okay well when you talk about only focusing on "the core subjects", what exactly are you referring to? The two main core subjects are Maths and English Language (not English Literature, which is what you would be reading A Christmas Carol for).
You've also stated Science. Which sciences... all three of them?
If you're going to be going back into school in Year 11 then your best bet would be to study all the subjects you'll be taking in school for your GCSEs. There's no point only focusing on "core subjects" because during Year 10 the other kids in school will be learning half the syllabus for around 10 subjects, as schools spread out the GCSE material over 2 years.
My advice would be to contact the school you plan to attend and ask them which exam boards they use, and work out which subjects you will be taking, and then plan to focus on ALL of those subjects whilst you're at home, otherwise when you get back to school you're going to be wildly unprepared for your exams.
Honestly going back to school in Year 11 is a terrible idea for reasons stated above - most home educated kids avoid it and schools generally don't like taking home educated kids on during Year 11 as most of the time they've missed half the GCSE material. If you were my kid I would just home educate you until the end of high school, and have you sit IGCSE English Language, IGCSE Maths, plus 3 other subjects of your choosing at a private exam centre as a private candidate, albeit having to bear the brunt of the exam costs.