You don't need a licence for most common domestic pets. You must make sure your dog is microchipped.
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Which UK Airlines Allow Pets In Cabin? The main 3 airlines that allow pets in the cabin are: KLM, Lufthansa and TUI. This only applies for very small pets that weigh less than 8kg and would have to be booked direct through the airline, without the assistance of a pet export company like Fetchapet.