Luke won on his first attempt in the competition in April 2017 at the age of 27. He did his stage at Nihonryori Ryugin in Tokyo, the first and, so far, the only winner to do a stage in Japan. He is now executive head chef at Le Manoir Aux Quat’ Saisons in Oxfordshire, saying the his return there in early 2023 felt "like a true homecoming" to the place at which he started his career.

When Luke won The Roux Scholarship, he was head chef at Dabbous and went on to works for Ollie Dabbous’ subsequent restaurant Hide in Mayfair, which won its first Michelin star in the 2019 guide after six months of opening. Luke left Hide in May 2019 and in April 2020 he took over Evelyn’s Table - a small, intimate counter restaurant in the heart of London, working alongside his brothers Nathaniel and Theodore. Their menus focused on British produce but used French and Japanese cooking techniques. In the 2022 Michelin Guide to the UK and Ireland, Evelyn's Table was awarded a Michelin star. In addition, the three Selby brothers jointly won the Young Chef of the Year Award.

2017 was a golden year for Luke: within weeks of his return from his stage in Japan, Luke competed in the final of the National Chef of the Year and won, making him just one of five previous Scholarship winners to win both competitions. He is also winner of the Academy of Culinary Arts Annual Awards of Excellence in 2012, the Annual Craft Guild of Chefs Graduate Awards in 2013 and the Young National Chef of the Year in 2014.

Luke always wanted to be a chef and worked at a hotel and a restaurant at weekends while he studied for his A’Levels. He then went to Le Manoir Aux Quat’ Saisons for a week’s work experience which confirmed his ambitions. After gaining A’Levels in chemistry, biology and art, he was offered a job as a commis chef at Le Manoir, rising from commis to sous chef over six years, running every section of the kitchen, the private dining room and the pass.

In September 2015, he took a job with Clare Smyth at the three-star Michelin Restaurant Gordon Ramsay in Chelsea, London. Leaving as Junior Sous in September 2016, he took a job with Ollie Dabbous at ‘Dabbous’ in Fitzrovia, London, starting as senior sous chef and rising to head chef within six months.