There was never any major issue in regard to trans people in the UK, that I'm aware of, prior to the far left losing the plot.
I think what you're referring to is a time when a very small number of men who suffered with gender dysphoria so greatly that they did their best to appear be women, were mostly politely humoured by society. Nobody, including the men, believed they had changed sex or could change sex, nobody said TWAW about these men.
A very few men therefore 'lived as women' i.e. wore dresses and wigs and makeup and chose female names and used women's facilities. Women, socialised to be kind and to fear male aggression, often played along with what all concerned knew was a pretence. Women did not consent to this, women were not consulted, our lesser physical strength and our female socialisation was exploited so that these men could feel better.
If you hadn't noticed, those days are long gone. Current TRAs call those men 'truscum' and look down on them. If this is the middle ground you think you've cleverly identified, think again. These men were prioritised over women and a lot of people looked the other way as it was a very very few and they were very very unhappy. And women don't really matter, in the scheme of things, if it's between a man feeling sad and a women feeling sad/scared/pissed off, no competition.
Those TW and those times, have been replaced by other TW and current times, and it wasn't women who caused the shift. Those TW were thrown under the bus along with women, gay people, confused adolescents, autistic teenagers, by the current incarnation of misogynist men, i.e. TRAs. This is their mess, not ours. We gave an inch, because no one bloody asked if we minded, and TRAs took 100000 miles.