If having the vaccine helps to stem the spread of the virus; it should also slow the development of different strains of the virus. With less people sick there should be less opportunity for it to mutate. Obviously added to the routines of hand sterilisation and social distance etc.
At least that's what I believe the idea is in principal. Only time will tell if it works! But the figures in the UKicon seem to point to a reasonably successful vaccination campaign.