The 3,000sq ft Waitrose store opened in the unit adjoining Ish and Anita Rattan's small Best One newsagents in June. The husband and wife retailing duo say that turnover has since slumped by 50%, leaving them facing closure.
"All we want is for Waitrose to stop selling news and mags, but so far we have received no response," said Anita.
The pair held a protest outside the store last week, and collected the signatures of more than 200 local residents.
Local councillor Colin Rosenstiel said he had no idea that Waitrose would "step on the toes of a local trader quite so sharply".
Ish and Anita are also battling their landlord, who owns the Waitrose unit, for failing to inform them of the multiple's plans.
The pair have been withholding their rent payments for the past four months and say that they plan to keep on doing so until they receive an explanation and apology from their landlord.
Waitrose said it was "unable to comment on the agreement between the landlord and another tenant", but explained that it hoped to attract more people to the area for the benefit of itself and its fellow traders.
Last month the same Waitrose store won a battle with the local council to sell alcohol between the hours of 11am and 11pm.
The store is in a 'cumulative impact zone' and an earlier attempt by Tesco to secure a licence for one of its stores was turned down.