Just checked and my health authority is claiming appointments would be within 2-3 weeks of referral receipt. Not sure If this means the appt itself or the letter inviting you to make an apt, but either way doesn't sound too bad.
Speech therapy waiting lists are very long in some parts of the country so you are far better to self refer and then you can always decline by the time you get to the top of the list for assessment. You wont get therapy unless you meet the criteria at the assessment so it is far better to check this if you have any doubts. It will only take 45 minutes of your time. In my experience it causes a delay with learning phonics at school and school would much prefer it is sorted first.
I'm an slt (but on maternity leave at the mo). What you describe sounds ok to be honest particularly as his language has been delayed. it can sometimes take time for children to sort their sounds out. You should find his sounds will develop as he learns more words and sentences. If you are still worried at 4.5 to 5 years old then ask for a referral as this is often the best time to start think about sound work (he's very little at the moment) the only exception being if you can't understand him all the time or if he is geting very frustrated on a regular basis then I would ask for him to be seen sooner. Getting tenses wrong is normal at this age as well.
My 3yr old was late to talk relatively speaking, saying about 2 or 3 words at the age of 2.
At 3.5years he has a good vocabulary and can make 5 or 6 word sentences, often with a few wrong words or tenses (seems fairly okay I think?).
But he is still having difficulty with some letters.
He can't say z and will use y instead eg puzzle is said puyyle
L is also tricky so Lego becomes something similar to yego
And the letters n, d and t are pronounced with the front of the tongue flat to the roof of the mouth, similar to a th in this.
There are a few more but I can remember them now.
I have seen that the z and l are usually grown out of, but I wondered what is going on with the d, n and t? None of my other children did this and I am not sure if it is something that the child grows out of or needs help with.