The Location Indicators are used, amongst other things, for sending messages like flight plans between ATC units. In days gone by messages were sent through a mechanical switching system that used the letters in the Indicator to route the message to more and more specific locations as you move to the right. Some was based on logic others were (
AFAIK) more arbitary.
Using Heathrow (EGLL) as an example - E indicates that the address is in the northern European region, G that it is in the UK (perhaps originally for Great Britain) and the latter two letters the specific aerodrome. I would guess that LL was used for Heathrow because it was
London's airport. The airports around Heathrow were allocated L for the third letter and a different fourth letter because messages destined for these airports went through Heathrow's switching centre. I can only guess that Gatwick got KK because it ends in K. Manchester is CC - your guess is as good as mine!
These days message switching is done by computers and the physical route of cables is largely irrelevant but the Location Indicators assigned years ago still stand. Those that are allocated today seem to follow a far more logical origination.
Well, that's what I got taught years ago and a bit of educated guesswork. Anyone else got any better reasons???