The present study makes a part of the already ample discussion on the subject of identification of the beginnings of severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) coronavirus pandemics in the world and considers the following question: do the anomalies in death rates in the earlier periods bring any new knowledge of the subject? With the ultimate purpose of answering this question, spatial differences are analysed of excess mortality for the first time at such a detailed spatial scale in Europe. As it is known, according to current knowledge, a strong increase in coronavirus disease‐2019 mortality occurred in Lombardy, Italy, from about mid‐March (Week 11–12 of 2020), followed by Spain and Belgium. It was decided, in the context of the present study, to see if similarly strong mortality anomalies, not assigned to this factor, were not present earlier. This could constitute circumstantial evidence that SARS‐CoV‐2 coronavirus was present in Europe on a much larger scale earlier than it is commonly believed. The study, therefore, looks at whether there were local outbreaks of elevated deaths between November 2019 and March 2020. The analysis used available Eurostat data for 34 European countries according to the NUTS1, NUTS2 and NUTS3 divisions based on 918 units with more than 100,000 inhabitants. The number of deaths was analysed over consecutive 24 weeks of autumn–winter (7 October 2019–22 March 2020, i.e., W41‐2019 to W12‐2020) and were compared with the respective data for the 3‐year reference period 2016–2018. The method used identifies geographically concentrated areas with excess deaths over short periods relative to the reference period. It was shown that 44 regions between W41‐2019 and W08‐2020 (i.e., before February 23) had elevated mortality (115% or more relative to the reference period). In the 44 NUTS3 regions mentioned, excess deaths during the autumn–winter period amounted to 96,000–126,000 when compared with the 2016–2018 baseline period (mainly in Spain, France, Italy, United Kingdom). It cannot be excluded that to some extent this could have been due to SARS‐CoV‐2 coronavirus infections. To confirm or deny this more clearly, detailed studies of the recorded causes of death in the indicated 44 regions are needed.