There appears to be some confusion above, despite Brains having given the correct answer in the first post.
At the age of 16 (in any part of the UK) a young person is entitled to walk out of their home and, if they so choose, never have any contact with their parents again. If their parents reported them as 'missing', and their location became known to the police, the police would be prohibited from telling the parents where their child was (although they could report that they were safe and well).
The rule about "16 with parental consent or 17 without it" refers to getting married, not to leaving home.
The age of 18 is irrelevant, except that a young person under the age of 18 can't enter into a legal contract without an adult guarantor (which could, for example, present practical difficulties for a young person trying to rent a bedsit).
Chris