My ds school was the same as yours and ds was very reluctant to do his phonics practice too but it’s really a good idea to help him at home, we aren’t talking 20 mins a day - just start with 5 mins and gently extend on the days when he’s more cooperative. You might not manage both phonics and writing at first while his concentration span is short. Make sure when you do it, you’re sitting at a table with no distractions and you are 100% focused on ds too.
My ds went from being unable to read or write a single letter at start of Reception to getting 38 out of 40 on his reading assessment in Y1 by doing just tiny bits of extra support at home it made a massive difference. There is no way he’d have made it without help at home.
I found the best time of day to do the phonics practice and writing was 7.50 a.m. after ds had eaten breakfast and dressed. He was far too tired to concentrate (he was in after school club every day).
We would do ten mins about 5 or 6 days per week. Occasionally ds would throw a real strop as he couldn’t face doing the homework because his friend told him he is stupid, or he found it too hard - mostly I’d just help him tough it out and despite tears we would get it done and I’d find a way to make him giggle and realise he’d done a great job. Good to learn some resilience as long as you don’t make it traumatising.
It has been good to see his confidence grow and now if he says “I am too stupid to do this” I just tickle him until he begs me to stop, and we move on.
For writing, ds was just tracing and copying letters on a worksheet so we’d just do one or two letters per day. Loads of encouragement and get some “well done/good job” stickers on a roll so he can have one when he tries hard (or frankly even when he doesn’t!). He liked wearing the sticker to school in the morning.
You can also try things like getting ds to draw the letters with his finger in a plate of flour or sand.
I also really recommend books of mazes and simple dot to dot puzzles as they are great for tracking a line and pencil control. Ds would often do a puzzle as a warm up before his writing.
Now my ds is in Y2 and he stoically puts up with his homework - although he always tries to push back, once he gets started he actually enjoys it. He has become a bit of a Times Table Rockstar fanatic and has perfected his 2, 5 and 10 multiple and division facts and steadily working through 3 and 11 at the moment. We are working on spelling now because that’s his next tricky area. He has come a long way since those slightly tearful days when he couldn’t do anything at all.
I never worked methodically like this with dd1 who is very able but my ds needs it. In a classroom where 15% + of the kids have SEN that make learning much harder, my ds doesn’t get quite as much attention so he definitely needs the top ups at home.
So don’t push too hard and as pp said, make it a habit - we just have it built into our routine so ds just knows it’s time for his reading, spelling and arithmetic in the same way he knows it’s time to brush his teeth and put on his coat and shoes.