Not so definitely, from reading the links.
The first link describes some form of sexual offense, but is only strict liability if the person is under 13. Quoting the link:
"A person(A) commits an offense if..."
"(c)either—
(i)B is under 18, and A does not reasonably believe that B is 18 or over, or
(ii)B is under 13."
The second link is an anti-prostitution offense, which does not match the theoretical example or Minsky's case, and is punishable by fine.
In England this is definitely illegal.
https://www.legislation.gov.uk/ukpga/2003/42/section/47
https://www.legislation.gov.uk/ukpga/2003/42/section/53A