Flights were suspended after the BMI aircraft from Frankfurt left the runway as it taxied to the terminal on Friday.
The Embraer 145 aircraft was moved late on Friday and Airport officials said they were working with airlines to resume flight schedules.
The Air Accidents Investigation Branch (AAIB) confirmed it was sending a team to the airport.
But a CAA spokesman said there was a duty on the airlines to provide reasonable "care and assistance" to passengers unable to travel.
This could include phone calls, meals, food and drink, or overnight hotel accommodation with transport to the airport.
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