Slovan Havlíčkův Brod subsequently netted £1.5 million following Souček's transfer to West Ham United in 2020, covering their running costs for the next ten years.

[2] Viktoria Žižkov’s manager, Jindřich Trpišovský, watched Souček play and was not convinced of his ability but was persuaded to take him on a loan costing nothing to the club.

However, in the 2016–17 season, his position in the first team was lost due to the arrival of Michael Ngadeu-Ngadjui and Souček played only 93 minutes in three months between September and December 2016.

[8] On 29 January 2020, Souček joined Premier League side West Ham United on an initial loan deal until the end of the 2019–20 season, with an option to make the transfer permanent in the summer.

[10] In West Ham's following league match, he scored again to give his team a 2–1 lead against Newcastle United, in an eventual 2–2 away draw.

[13] On 1 January 2021, Souček scored the first Premier League goal of 2021 as West Ham beat Everton 1–0 at Goodison Park.

[23] After representing the Czech Republic in several youth categories, Souček debuted for the senior team on 15 November 2016 in a friendly match against Denmark.