They form part of a strengthened DLKW Lowe creative team, with Helen Rhodes and Matt Lever also joining from Dare.
Cockrell and Storey were shareholders in Beta, but their stakes will now be distributed to other staff. Robert Campbell, a founding partner of Beta, said that he would be taking a more hands-on approach to the agency's creative output.
Cockrell and Storey have been a creative team since 1985 and have previously worked at D'Arcy Masius Benton & Bowles, Rainey Kelly Campbell Roalfe/Y&R and Abbott Mead Vickers BBDO. They have worked on campaigns for Sony, Orange and Asda. The pair joined Beta at its launch in 2010.
DLKW Lowe's executive creative director Richard Denney said: "Phil and Graham have produced highly awarded work for some of the best agencies in London. Their experience will make a valuable contribution towards us realising DLKW Lowe's creative ambition."
Rhodes and Lever started their careers at CDD and have also worked at TBWA\London. They were responsible for creating the Virgin Holidays "rockstar service" work at MCBD and the Department of Health "real kids" campaign.