Given the recent report out of Spain showing only 5% of those infected had any antibodies and reinfection is proven, I dont think there is any herd immunity. Same with vaccine, you can only achieve herd if people take the vaccine and its 100% successful
Don't think reinfection is proven yet, though looking more likely.
However, vaccines can offer longer resistance than infection in many cases (especially vs some of these mild cases I'd imagine).
Also, you don't need 100% for herd immunity, I think that the percentage for this virus is around 60%, it's not very transmissible when compared to something like measles.
From memory the oxford vaccine was 40% effective, but it may be much more than that with a booster, even if it's just the 40% again, that reaches the 60% (though of course it won't be 100% vaccine coverage).
However, even around 20-25% should start to see a significant effect on the r0 number, so when combined with other measures, should allow us to hit this on the head.