No. To travel from the UK to another EU country, your pet must be microchipped (although some countries accept a tattoo instead), vaccinated against rabies and issued with a pet passport. However if you wish your pet to return to the UK this will take at least six months for a blood test to confirm the rabies jab has taken properly. This can be done in another country, provided the first part above has been done before you leave.
Please note, the cargo hold has to be heated to a certain temperature, so you can only travel them on certain routes and flights (check with the airline). There are only certain airlines/routes which are authorised to carry animals. There may also be a limit to the number of animals they allow on any one flight, so make sure you book early. You also have to have a travel crate which meets certain criteria for size, ventilation and food/water containers. Some countries have other requirements such as worming/flea treatment before they will accept them.