In order to answer your question, I emailled Professor Richard Aldrich
who is the author of several books relating to the history of
education. He replied very promptly to my enquiry and advised that
co-educational classes have existed since medieval times.
However further searches revealed that although co-ed classes have
been around for literally ages, co-ed schools have not.
The first co-educational Boarding School in the UK was the Alfree
School in 1766. You can find the passage about half-way along the
following page although CTRL - F and then "Alfree" when on the page
will take you straight to it.
The Alfree School
Next was the Dollar Academy in Petersfield, which opened it's doors in
1818 and also claims to have been the first co-educational boarding
school in the UK.
Bedales school also claims to be the first co-educational boarding
school in the UK although it did not open up it's doors until
1893..but it appears that the accolade for first co-ed "public school"
is not contested.
Lydney Grammar School, was founded in 1903 and pre-dates many of the
other pretenders to the throne of first co-ed grammar school.
However, Lady Manners School, established in the 1890's claims to be
amongst the first technical grammar schools in the country.
Lady Manners School.
There are a few others that claim to be the first grammar schools, but
they are from the 1950's so they can't really argue the point
convincingly. Nor in fact do they try.
Search Keys "First Co-educational" UK Search.
Hope this helps.