The RMT union will now demand "urgent talks" with Network Rail and the 15 train operators which were balloted to find a negotiated settlement to the dispute over pay, jobs and safety.
Around 71% of those balloted took part in the vote with 89% voting in favour of strike action and 11% voting against.
Members of Govia Thameslink Rail (GTR), which runs Thameslink services to Gatwick and Luton as well as Southern Rail, which operates Gatwick Express services, voted against striking in favour of other forms of industrial action. Impacted services could also include Avanti trains to Birmingham International.
