Miley, who won gold and two silvers at the European Short Course Championships prior to the worlds in Turkey, topped the podium in the 400m medley on the first night while Jemma Lowe also added 200m butterfly bronze for Britain.
And, clearly keen to get among the medals herself, Allen was the quickest qualifier into the semi-finals of the 100m medley after touching home in a new personal best of 59.20 seconds, bettering her previous mark by 0.3.
That was 0.13 quicker than Plymouth-based Olympic 100m breaststroke champion Ruta Meilutyte in second and almost two seconds faster than Miley, who just sneaked into the semi-finals after placing 15th overall.
Allen and Miley, who has not raced a 100m medley in over three years, were the only individual British qualifiers on the second morning as Rebecca Turner, Roberto Pavoni and Matthew Johnson all missed out in their respective events.
With world long course silver medallist from 2009 Fran Halsall deciding not to compete in the 100m freestyle before the championships began, Turner was the sole Brit involved in the event and placed 25th in the heats in 54.97.
That was 0.70 shy of the 16th and final qualifier for the semi-finals Larissa Oliveira while, with heats leading straight to a final in the men's 400m medley, Pavoni and Johnson were off the pace despite both recording personal bests.
Pavoni ranked 14th in 4:11.17, nearly seven seconds behind quickest qualifier Seto Daiya, while Johnson, swimming at his first senior international championships, was four places lower in 4:13.75.
However there was joy for Pavoni as part of the British men's 4x200m freestyle relay quartet as he, Ieuan Lloyd, Chris Walker-Hebborn and Robbie Renwick finished third in their heat to advance to the final in seventh overall.
Lloyd lowered his own Welsh record to 1:45.26 on the opening leg as the British team clocked 7:06.50 overall in a heat involving America and Australia with Germany the fastest qualifiers in 6:58.67.
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