Still exist in the Deepest South, on the Portsmouth Direct Line at least. There are stations where the Ladies Lavatory is accessed via a smaller, separate, Ladies Waiting Room. To keep things simple the Waiting Room and Lavatory are collectively labelled 'Ladies'.
Milford is a classic in this regard. It has a civilised Ladies Waiting Room and Toilets in the main building. The Gents are wedged in a narrow gap between the Station Building and what looks like an old Lamp Hut (now a rather rustic Coffee Shop that also does things like early morning Porridge). The Gents urinals look like they were originally open to the sky and its Water Tank is a bitumen covered lashup on its roof. - the whole Gents setup looks like it hasn't been touched since 1940.
In the 1980s and '90s you often used to find stations with toilets for people of one sex only - more often a Gents but no Ladies, but occasionally the other way round. This was quite common at smaller stations on the London suburban network, especially on the Southern Region. There may still be a few stations where this is the case, but I haven't come across any for quite a while.
Probably until about the 1970s BR (and its predecessors) believed that it had a duty to provide toilets at almost every station except for unstaffed halts. After that their condition gradually deteriorated, partly because of falling levels of station staffing, until BR felt it had no choice but to pull the plug (or should I say pull the chain?). Presumably if the toilet for one sex became heavily vandalised or due major repairs, then it would be permanently closed while the one for the other sex would be kept open as long as it remained in working order. Often the Gents would only have a urinal (which was probably easier and cheaper to maintain and less easy to vandalise than a WC) with the WC cubicles padlocked out of use.
Sometimes BR would even demolish the main part of the platform building that used to house the waiting room etc, but leave the gents' toilet block standing and in use. I remember that being the case at West Dulwich and at least one station on the Faversham-Dover line (Selling, I think).
Where a toilet had recently been closed, you would often see the Ladies or Gentlemen sign covered up with a piece of paper, cardboard, parcel tape, or a black refuse sack. Sometimes you would also see "toilet no more" or something similar written on it (which could have been done by officialdom or by a graffiti artist).
These days it's more common for small stations to only have a disabled toilet (which can only be accessed with a RADAR key).