Haughton was extended to beat battling Nigerian Odejoke Dimbo 7-1, 7-4, 7-3 to reach the third round.
Coventry's Mark Constable, England's other entrant in the men's singles, breezed through to the last 64 with a 7-0, 7-0, 7-0 demolition job on Falkland Islander Doug Clark.
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