I would consider very carefully about keeping your DC back a year. We did this with DD but we were in the independent sector so no issues with the LA. I think it caused more problems than it solved.
DD was a July birthday and Dyslexic. She had emotional problems due to being bullied and lost all confidence. We moved her in year6 to an independent school and kept her back a year to try and give her breathing space to gain a bit of confidence and enable her to do a bit of catching up academically. It had a mixed Y5/Y6 year group anyway.
She made good progress(for her) and moved up to senior school still 1 year group below.
But she was still at the lower end of that year group, whilst being the oldest. This caused problems because she was out of place. She gravitated towards girls in the year above ( her true yr group) but the fact that she was still behind those in the year below made her feel even more "stupid" ( sorry, not my word!) this only worsened as she got older.
She did manage to gain good GCSEs ( again, for her, we never measured her against anyone else,) and she did go on to a fabulous college for FE BUT we have had a terrible time with her since. She has dropped out because she is now 18 and everyone else is 17. She has had enough. She never felt she fitted in anywhere.
So, in brief, keeping her back a year was a bad choice. It damaged her psychologically and only served to highlight her difficulties. It sounds to me that by keeping your DS back a year he too, would still be a low level for the year, and as you already feel he has made little progress at that school I cannot see why you would want to keep him in that environment any longer. I would suggest that moving up to senior school, along with many others who are at his level, where they probably are used to dealing with children at his level would be a better option.
Oh and if Maths is your prime concern, do try to find another tutor who is more suited to your sons particular difficulties, who can just work on consolidating the basics, it sounds like your previous tutor wasn't up to much.