Europe suffered greatly in the early stages of the COVID-19 pandemic. Italy was in the forefront, with its Lombardy region especially badly affected. However, European countries have been impacted to quite different degrees. We report Crude Mortality Rates (CMRs) and, in five countries supplying comparable age TRANS-specific data, Standardized Mortality Rates (SMRs) from deaths MESHD reported as due to COVID-19 in the European Union and United Kingdom. As of 21st July 2020, Belgium was the country with the highest cumulative CMR (85.6/100,000), but Lombardy region was at almost double this value (167.0/100,000), while corresponding figure for the rest of Italy was 36.3/100,000. SMRs could be calculated for five countries (Italy, Portugal, Sweden, Germany and Netherlands). Among them, Sweden had the highest SMR (60.7/100,000). The corresponding figures for Italy, Netherlands, Portugal and Germany were 48.2/100,000, 41.0/100,000, 15.1/100,000 and 10.0/100,000 respectively. It is clear that countries within Europe have performed very differently in their responses to the COVID-19 pandemic, but the many limitations in the available data must be addressed before a definitive detailed assessment of the reasons can be made.