In 1672, the Third Anglo-Dutch War broke out, which gave Spragge the chance to deal with his old rival Tromp. At this time, Rupert and Spragge became rivals, the latter becoming jealous for not having been appointed supreme commander. Spragge was in command of the Red Squadron on the "London" in the Battle of Solebay in 1672 and of the Blue Squadron on the new "Prince Royal" of 100 cannon in the double Battle of Schooneveld of 1673. In these last Schooneveld battles he sought out and fought Tromp, readmitted to the navy in 1673, with great fury, but without result.