OP, has he had any actual medical assessment? Just to expand on my pp, we had a HV referral when he was 3yrs old - and then we had physio first - which was unsuccessful because his tendons were so tight that he literally couldn't put his heels down to the floor (they had tightened because of persistent toe walking).
We then used private health insurance via a GP referral (because DH has it through his work) - but the same treatment would have been available on the NHS. We just got it done quickly, because we wanted the casts off before he started school. This was 10yrs ago - so treatment may have moved on a bit since then.
The casts stretch the tendons over about 8 weeks - he could walk, run, climb in the casts, and had 'cast shoes' which were fine. Once the casts came off, he had difficulty walking afterwards. His feet were kind of floppy, he had to re-learn. We had another course of physio, where he did stuff like walking on his heels, or 'penguin walking' to re-train his muscles. A couple of weeks of this - and he was walking well.
He was a habitual toe walker though - so did have to be reminded not to walk on tiptoe regularly. But I was actually watching him today, after reading this thread - and his walking is good - he puts his heels down, but he has quite a bouncy walk iyswim. I am very pleased we went with the casts.
There was no physical or neurological cause to his toe-walking. It was purely a habit.