ive never seen anyone handing out invitiations
At my DS school you give the invitations to the teacher and the teacher hands them out. Nobody would hand them out because a) like you, they don't know every single parent and b) it would be very divisive as not everyone can have a whole class party.
Dungeon the OP has children in Y1 and Y2. So one of her children has gone through 3 full years of school without ever asking to have a playdate, without ever being invited for one and without ever being invited to a single party.
That is NOT typical and says to me either the child needs a bit of help with friendships or the teachers are falling down on the job of making sure all children are included.
Incidentally we've only had 1 or 2 all-class parties in DS year (he's in Y1 - one mad mum invited both classes but the others were just 30).
There are a few new-to-the-UK or nervous-about-Halal-food parents who tend to say no to most invitations (one of the other mums and I have been working withe mum of a lovely little boy in one of those categories to persuade her it's OK to send her DS to parties), nobody expects those parents to reciprocate.
The majority have smaller parties so e.g. DS asked about 15 at his party and has been invited back to about 5 (one just has a foul parent who didn't invite DS despite the two boys being best pals, several will have had very small parties, a few just weren't that friendly after all).
Did you ask your DCs if they wanted parties? I know not everyone has the wherewithall to do them but maybe once every couple of years e.g. taking it in turns so one gets one each year and the others have a tea at home with just family?