According to reports, the lost luggage problems that have occurred at airport since the end of March have cost British Airways (BA) around £16 million.
Mr Tarling explained: "This particular company took the view that if you took out travel insurance after the problems at Terminal 5 became apparent, you would not be covered for baggage on the basis that it was a situation that was known to you.
"A number of insurers publicly said that they would continue to provide cover and that particular company, after speaking to BA, are happy that the situation is manageable."
Recent research by Sainsbury's Travel Insurance estimates that 10 per cent of people heading abroad this year may travel without cover.
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