Sheffield & Dearne AC member Thompson, aged 24, was part of the Great Britain team, which also included Cameron Chalmers, Joseph Brier and Michael Ohioze, that finished sixth in today’s heats.
The team finished with a season’s best time of 3:03.29.
All five teams ahead of the the British finished in under three minutes, with USA, Botswana and Trinidad and Tobago automatically qualifying for the final.
Thompson, an accountant, ran a personal best split time of 45.42 seconds in the mixed 4x400m semi-final last week, having previously anchored Team GB to bronze at the European Indoor Championships in March.
He was replaced by teammate Niclas Baker for the final.