The Europa League group stage entered its final matchday on Thursday and all the British teams secured their progress.
A youthful Liverpool may have been defeated by Union Saint-Gilloise in Belgium but it did not matter as Jurgen Klopp's side had already won the group.
The Hammers joined the Reds as group winners after easing past Freiburg at the London Stadium, meaning they will skip a play-off with one of the sides who dropped out of the Champions League earlier this week.
The two teams will be joined in the knockouts by Brighton, who got a last-gasp win over Marseille thanks to Joao Pedro's late goal at the Amex.
Rangers then followed, beating Real Betis 3-2 in Spain.