It is estimated that global anthropogenic carbon dioxide (CO2) emissions reduced by up to 12% at the start of 2020 compared to recent years due to the COVID-19 related downturn in economic activity. Despite the large decrease in CO2 emissions, no reduction in the trend in background atmospheric CO2 concentrations has been detected. So, how long would it take for sustained COVID-19 CO2 emission reductions to be detected in daily and monthly averaged local CO2 concentration measurements? CO2 concentration measurements for five measurement sites in the UK and Ireland are combined with meteorological numerical weather prediction data to build statistical models that can predict future CO2 concentrations. It is found that of the observed daily variability can be explained by these simple models. Emission reduction scenario experiments using these simple models illustrate that large daily and seasonal variability in local CO2 concentrations precludes the rapid emergence of a detectable signal. COVID-19 magnitude emissions reductions would only be detectable in the daily CO2 concentrations after at least 38 months and in monthly CO2 concentrations after 11 months of sustained reductions. For monthly CO2 concentrations the time of emergence is similar for all sites since the seasonal variability is largely driven by non-local fluxes of CO2 between the terrestrial biosphere and the atmosphere. The COVID-19 CO2 anthropogenic emissions reductions are similar in magnitude to those that are required to meet the Paris Agreement target of keeping global temperatures below C. This study demonstrates that, using measurements alone, there will be a considerable lag between changes in global anthropogenic emissions and a detected signal in local CO2 concentration trends. Thus, there is likely to be a delay of several years between changes in policy designed to meet CO2 anthropogenic emissions targets and our ability to detect the impact of these policies on CO2 concentrations using atmospheric measurements alone.