It takes longer to see a GP not 'cos of immigrants but 'cos GPs are greedy and want the capitation fee they get for each patient on the books of the practice.
That and folk don't directly pay so don't end up out of pocket if they make an appointment and cancel it.
When I was in France my GP in France was the old school single handed practice now prohibited in UK.
You turned up in the day...without need for any pre-booked appointment and he saw you.
It cost 20 € which you then we're re-imbursed through your Carte Vitale French state medical card.
Twas the same here at one time. I still say there are too many folk for the facilities.☻☻☻☻