Ryanair has amended its controversial new baggage policy to allow 2 million customers who had already booked flights to stow their wheelie cases for free.

Last month Europe’s biggest budget carrier announced wheelie cases under 10kg would no longer be allowed in its cabin from November, except for passengers booking priority boarding at a cost of £6 (or the same number of euros, €6). Others would have to pay £8 to check in a small case.

The airline said the move was necessary to reduce delays at boarding, but provoked outcry from passengers who had already booked flights for November onwards, and faced additional fees as well as a wait at the carousel at the airport.

Those passengers were given the option of cancelling flights for a full refund or adding priority boarding or stowing a small bag – with the airline adding insult to injury by charging them the higher rates of £8 or £10 for amending an existing booking.

With many passengers querying the legality of refusing to honour booking conditions, Ryanair has now conceded by allowing a 10kg bag to be checked in free, for all of the 2 million non-priority customers who booked before 31 August to travel after 1 November.

Around 50,000 passengers who had already booked and since bought priority boarding will also have the £8 fee refunded.

The airline said that all pre-booked passengers will not be penalised in any way by the changes.

Ryanair’s chief marketing officer, Kenny Jacobs, said: “As always Ryanair continues to lower the cost of travel, while our new bag policy from 1 November means we can eliminate all free gate bags and related flight delays.”

The change was the second time this year Ryanair had changed its luggage policy as it grappled with increasing numbers travelling with small, wheelie cases.