Three million booster vaccines have now been given to people across the South West - meaning 65% of those eligible have had a jab.
Centres across the region are encouraging more people to come forward to take up an earlier slot, including Greendale.
The site, which serves Exeter and East Devon has been staying open until late into the night.
"I think the way staff have stepped up has been absolutely amazing," nurse Susan Howell-Richardson told ITV News.
"We are all working extremely long hours, many more than we normally do. I think many of my colleagues have worked until midnight, but it's all been worth it.
Electrician John Fallon now spends every other night at the site after work, having trained as a vaccinator with St John Ambulance.
"It feels good to be involved in a national effort, and also, I don't like injections myself and being a part of it has taken away the fear of it.
"I inject so many people now that I can hardly complain myself."
Last week walk-in appointments were turned away because the centre could not cope with the huge number of people arriving for their boosters. But demand has since faded.
Queues are short, and a new access road has been built. Staff say the measures have resulted in more unvaccinated patients coming forward.
"We're seeing a real increase in the number of first doses, which is just great to see," said Operational Lead Leigh Mansfield.
"We encourage anybody that hasn't yet had a vaccination to come for their first dose. Even if somebody has had a long gap between the first and are yet to have their second, it's never too late.
"We've really stepped up to increase the capacity in the programme, so there is a lot of availability and a lot of different venues."