"West Ham United have been asked by the police to postpone the first-round tie with Aldershot Town tomorrow night," a West Ham statement said on Monday.
"The club were contacted this evening and told that all major public events in London were to be rearranged because of the need to focus police resources elsewhere."
A statement from south London club Charlton added: "With rioting taking place across London, officials were in contact with police throughout Monday evening. Clearly the most important factor is people's safety. The police have told us they believe the match should be postponed on safety grounds."
Crystal Palace's cup tie with Crawley Town in south London could also be under threat.
England [ Images ] are due to play the Netherlands in a friendly in north London's Wembley Stadium on Wednesday.