In reply to Ben_Climber:
You cannot walk up Kili without a local guide. If you want to do it as inexpensive as possible you could get a guide on your way to the gate when you sign in at the park but then there are masses of unknowns in doing it that way.
Alternatively, a Tanzanian based company will do all the logistics and guide you up the mountain. A few have been suggested on some of the posts above.
Finally you could choose a UK based company to take care of the logistics and guide you up the mountain. Exodus, Jagged Globe or Hepworth Adventures will do that for you. Feedback from the last provider is very positive from people who have been on previous trips. Https://hepworthadventures.co.uk/Kili
But, I should be honest and declare an interest in the last company mentioned and hyperlink provided!
Thanks
Jeremy