I'm a US citizen and I am visiting the UK. My passport stamp is illegible, although it says "you have __ months leave to remain in the UK" - the number is completely illegible. I am aware I'm allowed 6 months, but I need this to be clearly stamped in my passport. Where I should go, or whom should I contact to get this verified? Thanks guys!
The absence of handwriting on the stamp indicates that the leave-to-enter is 6 months (Paragraph 23A of the rules).
Where I should go, or whom should I contact to get this verified?
There is no need to read the blurred text in light of the rules cited above. But there are several paths you can pursue anyway...
If you are already inside the UK, you can take your passport to a Citizens Advice Bureau and ask for a Level 3 Adviser. Many CAB's have at least one such person, and they will be able to take your enquiry further if they cannot answer it on the spot.
If you are outside of the UK, you can submit a Subject Access Request.
Or you can ask the Immigration Officer at your next landing interview.
As you are currently in the UK, you can safely assume that your leave-to-enter will expire at midnight 21 Jan 2018.
That is a standard UK admission stamp for a tourist, here is a slightly clearer image of one that Google found. It says you can stay for six months, or until 21 Jan 2018 given their definition of "six months".