The FA will be guided by police advice, but at this stage is planning for Wednesday's game to go ahead.
West Ham said in a statement that they were informed by police that "all major public events in London were to be rearranged because of the need to focus police resources elsewhere."
A Metropolitan Police spokesman said they were aware of the West Ham statement, but were unable to comment on any potential impact on the England game at this stage.
In London, violence broke out for a third consecutive day with riot police deployed and firefighters tackling blazes across the capital, following disturbances in Tottenham on Saturday evening and Enfield on Sunday night.
Shops were looted and buildings, among them a furniture store in Croydon, set alight as police clashed with youths.
Police in riot gear were also deployed in Birmingham city centre after scores of youths rampaged through the shopping area, smashing windows and looting from shops.
The England cricket team are currently based in Birmingham ahead of the third Test against India, which begins at Edgbaston on Wednesday.
BBC sports news reporter Joe Wilson said that nearby hotels had been advised to lock their doors.
He wrote on Twitter: "Helicopters circling over Bull Ring, about half mile from England hotel. Spoke to England head of security, confident all players safe."
Meanwhile, BBC sports news reporter Leon Mann tweeted: "Organisers of Ghana v Nigeria tell me game still set to go ahead tomorrow at Watford FC as planned."
Clearly the most important factor is the people's safety
Charlton chief executive Stephen Kavanagh
West Ham's game was the first to be called off, and the club announced on their website: "West Ham United have been asked by the police to postpone the Carling Cup first-round tie with Aldershot Town tomorrow night.
"The club were contacted this evening and whilst neither the club or police anticipate any issues around the game itself, the club has to comply with the police request.
"No date has yet been set for the rearranged match but the club will be in contact with the Football League and Aldershot."
A statement from Aldershot read: "We understand many supporters will be disappointed with this announcement but confirm that the matter is out of the control of both West Ham United and Aldershot Town."
Charlton's stadium, The Valley, is close to Lewisham where rioting occurred on Monday.
A statement on Charlton's website read: "Given the events in London, the police have taken the sensible decision and postponed the match at The Valley, with Greenwich Borough Police Commander Richard Wood advising the Addicks at 2255 BST on Monday that the match should be called off on safety grounds."
Addicks chief executive Stephen Kavanagh said: 'We've been monitoring the situation as it's been developing all evening and have been in constant contact with police.
"Clearly the most important factor is the people's safety. The police have told us they believe the match should be postponed on safety grounds and obviously we have taken that advice."