Horsham were granted a walkover into round three of the Senior Vase on Saturday.
Middlesex-based Grasshoppers contacted the club to advise that they could not raise a front row and therefore wished to pull out.
The competition provides Horsham with the opportunity of playing at Twickenham for the first time in their history should this cup run continue.
The draw for the next round was made on Wednesday and the Green and Whites now face a trip to Watford-based Fullerians on January 3.
As part of the pyramid structure of league rugby in England, participants in the Senior Vase play in equivalent standard leagues across the country and with the Green and Whites currently heading their London league they are one of the favourites to go far in this tournament.
League leaders Horsham’s next game in London 3 South East is away to Folkestone on Saturday, who currently lie fourth in the table and traditionally provide tough opponents with league honours shared last season.
Pulborough also return to action this weekend after a free week with a trip to Old Dunstonians.
Pulborough sit eighth in the 12-team league and their hosts occupy fifth.