The Association of British Travel Agents said yesterday most flights were back to normal, and the backlog of delayed travellers was starting to decrease.
Andrew Grant, of Oxenhope, near Keighley, had been trapped in Kuala Lumpur with his young family, but was on his way back to Yorkshire last night.
Mr Grant's mother Margaret McGuinness said her son and his partner had been "frantic" after being delayed with their baby daughter and son, seven.
The family had been on holiday to Australia and a short stopover was planned in the Malaysian capital, but the ash cloud meant they were stuck for a week.
Mrs McGuinness, of Harrogate, said: "They were told the first flight available was May 6, and the airline said seats on an earlier flight would cost 3,000.
"Prices for everything were increasing tremendously and Andrew and his partner Janine were very worried that they were going to run out of money.
"They had travelled to Australia to visit Janine's grandmother, and they were due back in Britain last Friday. More than a week later they were still trapped."
Mrs McGuinness said her 47-year-old son, a teacher at Bradford's Southfield School, was desperate to return to work to help students prepare for exams.
Mr Grant, who was communicating with his family by text message, said he had received little help from the British embassy, and had watched as French nationals were put on flights by their consular officials.
Mrs McGuinness added: "They were frantic because they were only eating rice and had to downgrade to a much cheaper hotel room to eke out the funds.
"The airline contacted them on Saturday to say some seats had become available, but when they got to the airport the flight had been cancelled again.
"Andrew said he kicked up such a fuss that they put them on a plane at about 9am our time on Sunday morning and they are expected back on Monday."
According to industry figures released yesterday there were still 2,000 passengers stranded in Malaysia, alongside 10,000 in Egypt, 9,000 in Florida, 5,000 in South Africa, 4,000 in California and 2,500 in Thailand.
Budget airline easyJet said early yesterday that stranded passengers would be home by the end of the weekend.
Chief executive Andy Harrison said: "Bringing 200,000 passengers home has required a massive airlift, and I thank our passengers for their patience and understanding during this unprecedented natural disaster."
Yesterday, Virgin Atlantic boss Sir Richard Branson condemned ash cloud flight restrictions as an "over-reaction".
Sir Richard blamed the Government for grounding planes for six days when "all the experts" were saying there was "no danger at all to flying".
And he insisted the Government should organise compensation for the airline industry which has itself been paying for stranded passengers' accommodation and food.
Transport Secretary Lord Adonis said the European Commission was considering proposals on compensation. Airlines are on track to lose more than 1.3bn.