It also gives greater hope that vaccines will generate long-term immunity.
Previous studies have shown that Sars - a similar virus to coronavirus - can induce a T-cell response that lasts 10 years, but it was unknown whether a cellular response also happened in Covid.
Dr Shamez Ladhani, consultant epidemiologist at PHE and the study's author, said: "Cellular immunity is a complex but potentially very significant piece of the Covid-19 puzzle.
"Early results show that T-cell responses may outlast the initial antibody response, which could have a significant impact on Covid vaccine development and immunity research."
The study tested 100 NHS workers who had Covid but were asymptomatic or who had very mild disease.
Researchers found that the T-cell response was 50 per cent higher in symptomatic people, which could mean asymptomatic individuals will not be as protected in the future, or simply that they are able to battle the disease more efficiently.
The authors said that even when antibodies appeared to have gone, they were probably still there in low numbers, and able to be triggered quickly, in the event of a new infection.
Professor Paul Moss, UK Coronavirus Immunology Consortium lead from the University of Birmingham, said: "To our knowledge, our study is the first in the world to show robust cellular immunity remains at six months after infection in individuals who experienced mild/moderate or asymptomatic Covid-19."
Ladhani said it was likely there was a cohort of people who catch coronavirus but never develop an antibody response and that testing T-cell immunity may be a better marker for finding out how many people have had the virus.
Professor Charles Bangham, Chair of Immunology, at Imperial College London, said the results were "reassuring".
The research has not yet been peer reviewed and was published on the pre-print website bioRxiv.
