The simple answer is - no.
As an outdoor kitchen is considered a garden enhancement rather than a permanent structure, much like outdoor living room ideas, special permits or planning permissions aren't required.
Having said that, we would advise that any gas, electric or plumbing work needs to be completed by a professional.
The only time you would need permission in the UK, is if you are building a shelter. If you are within two meters of your neighbours border, you are not allowed to go over 2.5 meters high. Once you get to about 4 meters away, you can then go up to about 4 meters to the apex of the roof. You can always check with your local Council - go online and see what their rules and regulations are in your area.