Obviously nobody can know this as even those who had the vaccines in trial have had it under a year.
What they do know though is that antibodies are present in those who had it 3 or 4 months ago at the start of the vaccination programme here - so it seems reasonable that we can say that long and likely more. There as yet seems little sign that these numbers wane fast.
I do not think anybody expects this to be a one shot and out solution as the virus has shown itself adept at mutating into strains that get around barriers. The variant first identified in Kent that sent the Southern UK rates skyrocketing in December is now dominant across Europe (hence theur new lockdowns as they are way behind in vaccinating) and others will emerge.
Quite likely some degree of protection will remain even to new ones but it is equally probable that an annual booster jab for the vulnerable will be happening around September/October this year and possibly every year alongside the flu jabs for the ones who are in the priority groups as now. And likely on sale for about £10 to anyone else at Boots like the flu jabs are also. Just to protect over coming winters from the latest variants that have emerged in past months.
This is exactly what happens with the Winter flu jab already. We base it on the new versions that emerged in the Summer where in Australia and other Southern Hemisphere countries they have already hd their winter so they know what new variants if flu appeared in that time.