At the Berlin International Swim Meet when Taylor 14 years old, (in 2010) she swam a personal best in the 100 metres breaststroke, and finished in third place to "show her potential". In 2012, her first domestic "breakthrough" was at the London held 2012 British Gas Swimming Championships, where she finished fourth. She soon performed at an international level, at the 2012 European Junior Swimming Championships in Antwerp, Belgium. This was Taylor's first European Junior Swimming Championships, but she ended with a silver medal and a bronze medal, from the 50 metres breaststroke and the 200 metres breaststroke respectively. Taylor finished in third place in the 50 metres, 100 metres, and 200 metres breaststroke in 2013 at the British Gas Swimming Championships. Later in the year, at the 2013 FINA World Junior Swimming Championships, she won another bronze, this time in the 200 metres breaststroke, but coupled with two silver medals in the 4 × 100 m Medley Relay, and the 100 metres breaststroke.