Members plan to walk out for four separate five-day strikes as part of a bitter dispute over cost-cutting plans.
The first strike will begin on 18 May, ending on 22 May, with further strikes planned on 24 May, 30 May and 5 June.
But the union said BA could still prevent the walk-outs if it opened what it called "meaningful negotiations".
The dates were announced on Monday.
The newly-announced industrial action has the potential to disrupt travel plans for thousands as staff will walk out for a total of 20 days, covering spring bank holiday and school half-term holidays.
Football fans planning to fly out to the World Cup in South Africa could also be affected, with the last of the five-day stoppages beginning on the first weekend of the tournament.
However England's first game against the United States kicks off on 12 June, after the final strike has ended.
Unite members rejected a fresh deal for cabin crew earlier this month.
In a statement, Unite's joint general secretaries Derek Simpson and Tony Woodley blamed BA for forcing cabin crew to again resort to industrial action.
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There is little sign that either side is prepared to make the concessions needed to end this bitter dispute”
BBC employment correspondent
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"There can be no industrial peace without meaningful negotiations and while management victimises trade unionists and uses disciplinary procedures in a witch-hunt," they said, claiming that a Unite approach made over the weekend had been rejected.
"The seven days' notice period is sufficient time for BA management to do the sensible thing and reopen meaningful negotiations," they added.
BA defended its approach to the latest...