The airline will not be able to operate any short haul services from Heathrow today (Tuesday) as originally planned.
The continuing restrictions also mean the airline has been forced to cancel earlier plans to operate some long haul flights from Heathrow today.
BA hopes to run a number of inbound long haul flights, subject to airspace restrictions.
"We hope to reach a position soon where we can begin repatriating customers in large numbers," a statement said.
"The continuing restrictions have forced us to cancel our earlier plans to operate some short haul and some long haul departures from Heathrow today."
BA, showing obvious frustration at the ongoing grounding of flights, said: "We hope that on the basis of the data provided by the industry, the CAA will be in a position to direct National Air Traffic Services to reopen UK airspace and allow British Airways to operate flights into and out of the UK.
"We will only operate flights where we have assessed the situation to be safe in accordance with all our normal operating procedures, which are based on many years of of experience of operating in areas of volcanic activity around the world."
BA said: "Despite the fact that airspace over most European countries is open, UK airspace remains effectively closed."
People booked to travel on a cancelled flight can claim a full refund or rebook their flight for a later date.
BA earlier warned of delays even when flights do resume as it has more than 80 aircraft and almost 3,000 cabin crew and pilots out of position overseas across its global network.
"All of these aircraft will require detailed checks before they are cleared to enter service again.
"Inevitably, this will mean some delays and we ask for our customers’ patience and understanding in these very difficult circumstances."
Thomson Airways said all outbound flights from the UK would remain cancelled up to and including Wednesday.
A spokesman for airports operator BAA said: "The decision to lift airspace restrictions will be taken by others, and as things stand all flights at Heathrow, Stansted and Southampton airports remain suspended.
"When airports do open for business, we will continue to strongly advise passengers that they must check the status of their flight with airlines before travelling to airports.
"We appreciate the continued patience of our passengers at this difficult time and are doing everything we can to support airlines as they prepare to start operations."
Manchester Airport doe not expect to open until 19:00 today at the earliest.
"Unfortunately, the latest forecasts indicate that a further deterioration in conditions is likely," a spokesman said.
by Phil Davies
