How did Gatwick get to be EGKK ?
In the UK, having the 3rd and 4th letters the same seems to be a mark of being a major airport - or thinking you are. In the first category, EGLL, EGKK ( which is in the part of England where K is frequently the 3rd letter, e.g. EGKA Shoreham, EGKB Biggin Hill, EGKR Redhill), so to make it KK was, I guess, an easy choice. Also in the first group, EGCC.
You can get a good head of steam going over some others - EGAA, EGBB, EGHH.
Taking cover!