Teaser 3023: Timely coincidence

From The Sunday Times, 30th August 2020 [link]

George and Martha possess two digital “clocks”, each having six digits. One displays the time on a 24-hour basis in the format hh mm ss, typically 15 18 45, and the other displays the date in the format dd mm yy, typically 18 07 14.

On one occasion, George walked into the room to find that the two “clocks” displayed identical readings. Martha commented that the long-term (400-year) average chance of that happening was 1 in just over a six-digit number. That six-digit number gives the birth date of one their daughters.

On what date was that daughter born?