Soham exited the Alan Turvey League Cup in the first round, losing heavily at home.
Regent opened the scoring in the seventh minute when Jake Turner curled a freekick into the top corner, before doubling their advantage five minutes later through Josh Gould.
They made sure of their place in the second round in the 66th minute when Luke Read was given room to place his shot wide of the Soham keeper.
Brightlingsea will travel to either Needham Market or Heybridge Swifts in the second round of the cup.
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