The action, which was bound to lead to flight cancellations, was taken after some BA staff stopped work in sympathy with staff sacked by the Gate Gourmet company which supplies food to BA flights.
"We have had to suspend check-in for all our flights at Heathrow Terminal 1 and Terminal 4," a BA spokeswoman said.
The effective suspension of flights by BA followed attempts to halt the dispute which began yesterday.
The Transport and General Workers Union said 800 workers at Gate Gourmet had been sacked.
Earlier, BA handed out bags of food and gave vouchers to passengers so they could buy food and drink before they boarded flights today.
The airline had said a number of long-haul and short-haul flights were taking off from Heathrow with a "basic level" of catering on board - mainly water, tea and coffee. Refreshments were also served in airport lounges.
The union's general secretary, Tony Woodley, had warned of a possible escalation of the dispute and called on BA to put pressure on the American-owned catering firm to return to the negotiating table.
He accused Gate Gourmet of behaving in a "disgraceful" fashion and said it had unilaterally decided to reduce the pay and conditions of its staff.
"It does not want to talk and it does not want to compromise. It is a classic American union-busting exercise. BA must put pressure on this company."
The union said there was no blame on BA, but called on the airline to pressurise Gate Gourmet to stop the dispute continuing.
Gate Gourmet also provides in-flight catering at other airports across the UK, including Gatwick, Glasgow, Bristol and Newcastle.
The company said it was trying to change outdated working practices to improve productivity in the face of huge losses, and claims workers at Heathrow staged an unofficial strike yesterday which led to the dispute.
The company insisted today that the workers who had been sacked would remain sacked.
The BA chief executive Rod Eddington said earlier that the airline was taking an active role in trying to encourage both sides in the dispute to reach a speedy resolution.
He said he was "encouraging both sides to continue talking in a bid to settle their differences as soon as possible".
A Heathrow Airport spokesman said tonight: "The continuing industrial difficulties at Gate Gourmet have escalated, resulting in a stoppage by some British Airways staff.
"As a consequence, there is likely to be considerable delays to British Airways services for the rest of the day. If you are due to fly with British Airways in the next 24 hours then you are advised to contact the airline direct.
"There may be some disruption to other airlines but we are working hard to minimise disruption to passengers. If you are concerned about the status of your flight then you are advised to contact your airline."
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