Individuals with likely exposure to the highly infectious SARS-CoV-2 do not necessarily develop PCR or antibody positivity, suggesting some may clear sub-clinical infection before seroconversion. T cells can contribute to the rapid clearance of SARS-CoV-2 and other coronavirus infections1-5. We hypothesised that pre-existing memory T cell responses, with cross-protective potential against SARS-CoV-26-12, would expand in vivo to mediate rapid viral control, potentially aborting infection. We studied T cells against the replication transcription complex (RTC) of SARS-CoV-2 since this is transcribed first in the viral life cycle13-15 and should be highly conserved. We measured SARS-CoV-2-reactive T cells in a cohort of intensively monitored healthcare workers (HCW) who remained repeatedly negative by PCR, antibody binding, and neutralisation for SARS-CoV-2 (exposed seronegative, ES). 16-weeks post-recruitment, ES had memory T cells that were stronger and more multispecific than an unexposed pre-pandemic cohort, and more frequently directed against the RTC than the structural protein-dominated responses seen post-detectable infection (matched concurrent cohort). The postulate that HCW with the strongest RTC-specific T cells had an abortive infection was supported by a low-level increase in IFI27 transcript, a robust early innate signature of SARS-CoV-2 infection16. We showed that the RNA-polymerase within RTC was the largest region of high sequence conservation across human seasonal coronaviruses (HCoV) and was preferentially targeted by T cells from UK and Singapore pre-pandemic cohorts and from ES. RTC epitope-specific T cells capable of cross-recognising HCoV variants were identified in ES. Longitudinal samples from ES and an additional validation cohort, showed pre-existing RNA-polymerase-specific T cells expanded in vivo following SARS-CoV-2 exposure, becoming enriched in the memory response of those with abortive compared to overt infection. In summary, we provide evidence of abortive seronegative SARS-CoV-2 infection with expansion of cross-reactive RTC-specific T cells, highlighting these highly conserved proteins as targets for future vaccines against endemic and emerging Coronaviridae.