Last week a tribunal ordered the council to re-employ housing caretaker Ian Dell, but advised he should be moved to a job which 'will not bring him into any sort of contact, direct or indirect, with racial minorities'.
John Fahy, Greenwich housing chairman, said the council was examining possible grounds for appeal.
The judgment indicates Greenwich was mistaken in dismissing Mr Dell because of his racist behaviour, not his BNP membership.
Mr Dell was called to a disciplinary hearing last October after he was seen on Sky television chanting 'rights for whites' and selling the BNP newspaper in Tower Hamlets.
He was eventually dismissed on the grounds his action had destroyed the council's confidence in his ability to handle the concerns of ethnic minorities where he was caretaker.