The European winters of 2017-18 and 2018-19 were not climatically extreme, but both winters had a major sudden stratospheric warming (SSW). In February 2018, an SSW led to an intense cold outbreak across Europe and further spells of cold weather in March. The SSW of January 2019, although well predicted and expected to increase the chance of a cold end to winter, apparently produced little impact. In this study, we examine the performance of the Met Office seasonal prediction system in these winters, and the influences that led to these outcomes. To achieve this latter objective, sets of numerical experiments are performed in which the tropical troposphere and the extratropical stratosphere are relaxed towards their observed state, allowing the influence of each on the North Atlantic-European atmospheric circulation to be identified. Using these experiments, we show that the SSWs had similar impacts in each case, creating a signal of easterly surface wind anomalies in the weeks following the event. In contrast, tropical influences were opposite in the two winters, acting to strengthen the easterly signal at the end of February 2018 and opposing it in January 2019. The different apparent responses to the two events therefore came about largely through tropical tropospheric variability. Furthermore, we highlight the importance of a very strong cycle of the Madden-Julian Oscillation (MJO) in late January and early February 2018 as an important driver for the February 2018 SSW. MJO teleconnections appear to have been critical in creating the large mid-latitude wave 2 amplitude that has been identified as the immediate cause of this event.