The other Ryman South 'giant-killers', Maidstone, will travel to Bedford Town.
East Thurrock host Thurock in an all-Ryman Premier local derby, while last season's semi-finalists Wealdstone have been drawn away to Merstham.
The full draw for Ryman clubs:
Bedford Town v Maidstone United
Bognor Regis Town v Bridgwater Town or Hemel Hempstead Town
Brentwood Town v Lewes
Bury Town or Whitehawk v Grays Athletic or Ashford Town (Middx)
Concord Rangers v Enfield Town
Cray Wanderers v Arlesey Town
East Thurrock United v Thurrock
Hampton & Richmond Borough or Hythe Town v Three Bridges
King's Lynn Town v Carshalton Athletic
Kingstonian v Burnham
Leiston v Metropolitan Police
Merstham v Wealdstone
Soham Town Rangers v Ramsgate
Uxbridge or Royston Town v Canvey Island or Wroxham
Whitstable Town v Leatherhead
Wingate & Finchley v Hitchin Town
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