I'm not entirely sure what rights you think women have in UK law which are specific to women, unless you count things like maternity pay which are clearly not under threat due to trans inclusion.
You clearly haven't thought very deeply about this, but I suppose many women take their rights for granted, so I will give you the benefit of the doubt.
It's important to remember that TRAs aren't just asking for trans women to share services, they are going further than that and insisting that women as a sex have no shared qualities - that 'Trans women are women' and that pregnancy is not a condition that only affects women.
There is no reason to believe that any right will exist in perpetuity. We have maternity pay because of the impact of pregnancy on women and their ability to work, and because women can organise as a sex. Pregnancy is temporary and only ever affects a small minority of people at any one time. Take away the ability to talk about sex, and why give this small group of people special considerations? It's not as though there is a right to maternity pay in the US.
However, maternity pay and leave are also a double edged sword. They mean both that women can afford to become pregnant, and that employing women is potentially more expensive for employers. Like it or not more than 80% of women have children (if they didn't there would be an impact on population that would not be without consequence) and they tend to have children between the ages of 25 and 35, exactly the years when most people are trying to find employment and get promotion.
An employer trying to avoid expense can simply choose candidates who won't have to take maternity leave. Of course men can now take parental leave (although that isn't yet paid), but a man won't have to take time off because of e.g. SPD or high blood pressure and no provision will need to be made for breast feeding.
However, because of equalities legislation, it is illegal to discriminate in this way. However, take away the protected characteristic of sex and there is no discrimination. Again, referring back to the Lib Dems, if even talking about women in terms of female biology is transphobic, protecting sex based rights is impossible.
I agree that any one who is perceived to be female can face discrimination on that basis, but equalities law already covers people who face discrimination because they are perceived to have a particular quality.
There are many more examples, the most obvious being sport.
This shouldn't be a problem. Again I'm not being excluded if I can't get an over 60 bus pass. Protected Characteristics are not judgements of value. The exceptions just recognise that different groups have different needs.