The long-running dispute between British Airways and its cabin crew could finally be drawing to a close after the Unite union postponed a strike ballot due tomorrow and put an offer from the airline to its cabin crew members.

BA welcomed Unite’s move calling it “a genuine opportunity” to end the row that had threaten to cause further disruption over the peak summer holiday period.

The union was due to begin balloting tomorrow unless there was a breakthrough in the dispute, which has seen 22 days of strike action since March and plunged the loss-making carrier into further trouble.

However Unite leader Tony Woodley said he would not be recommending the offer as it failed to reinstate travel perks.

One union source said: “It is too soon to think that this is the beginning of the end. It is a bit more of a high stakes poker game. Let the company see the whites of our eyes. Let’s put it to our members and the company will be able to see exactly what people think of this.”

But even if members reject the offer, the delay to the ballot process will put off any walkout until after the peak of the summer season.

On Friday BA proposed a fresh offer that includes changes to pay structures that the airline says address cabin crew concerns.

These include new “top-up” payments and two years of guaranteed rises in basic salary from 2011.

Tony Woodly described the offer as “interesting” and said it would be “inexplicable if we didn’t put this offer to our members at this stage”.

However, BA has withdrawn travel concessions for striking cabin crew, and Mr Woodley said the reinstatement of these was still central to resolving the dispute.

In an interview with the BBC he said: “As a consequence of the company’s last and final offer the union and its representatives will have no choice but to delay our vote in order to allow our members to consult on the offer.”

But he said that failure to restore staff travel arrangements for cabin crew “prevents this offer from BA being the breakthrough everyone seeks”.

Nevertheless, BA said it welcomed Unite’s postponement of the ballot.

“We welcome this statement from the Unite leadership. We believe our offer is fair and reasonable and provides a genuine opportunity to end this dispute,” BA said in a statement.

Business Secretary Vince Cable described Unite’s move as “very good news” and “long overdue”.

Meanwhile, BA has begun recruiting 1,250 cabin crew on lower terms and conditions. Fears of just such a move were a driving force of the dispute, but Unite could not list the so-called “new fleet” as a grievance, for fear of a legal challenge.