That seems very late - my DS3 was referred to Speech Therapy when he was 15mo, and was seen for his first appointment when he was 21mo.
He is starting intensive speech therapy at the end of January, when he turns two.
I would see your GP and REQUEST a referral to Speech and Language therapy. If by the time he gets to the top of the waiting list he is fine, then you can always cancel the appointment!
Three is far too late IMO. And DS3 is the third out of my four DC's to have needed SALT. (Probable genetic issue)
DD was seen at 2yo, speech is normal. DS1 had no speech difficulties, in fact was a very early talker. DS2 wasn't seen until he was over 4 as my PCT had no speech therapist at that time - and he has lasting speech and language issues even now at 9yo. DS3 has been seen for an initial assessment, and starts therapy at 2yo.
I fully believe that waiting until he is 3yo is an unacceptable delay.
Does he babble? That is an important first step. Does he understand what YOU say to him? Can he follow a simple instruction like "give me that bottle please" if he is holding a bottle? Does he try to communicate in other, non-verbal ways like putting things into your hand if he wants something, or pulling you to the fridge if he is hungry? Does he try to talk but you can't understand the words? Or is he still not trying to communicate at all except crying and whinging?
This is all information that can help the speech therapist to make his or her initial assessment.
On a positive note - Makaton signing combined with speaking can help. Something Special is good to watch, and there are a lot of Makaton resources on the CBeebies website.
I have had to 'sign and say' with all of my DC's that have had speech delays, and it has really helped. Now they all talk, even DS2, the only lingering problem with my 14yo DD are about 3 words that she consistently mispronounces, DS2 has more issues, but I'm convinced that that is a lot to do with the delay in him receiving Speech Therapy.
I wouldn't take no for an answer tbh, if he has no words at 2.2yo, then he has a fairly significant speech delay, the reasons for which should be investigated by a Speech Therapist.
At 21mo, my DS3 had 3 words and was assessed as having a full year Speech delay - so no words at all at 5 months older than that is IMO and IME rather concerning.
Is there another HV you can see - at a weighing clinic possibly? For a second opinion? I really, REALLY would not be happy to wait until 3yo for a referral - some areas can have a 6 month or more waiting list for Speech Therapy, that's a hell of a lot of time to lose!