At present, the Equality Act allows for the provision of single sex services and spaces where there is reason to do so. You are also right that at present, the Equality Act allows anyone claiming to be trans (whether or not they have a GRC) to be treated as their adopted gender. Where it is proportionate to do so, it is still permitted to exclude a transgender person from single-sex provisions. In practice, many organisations either don't understand or are fearful of maintaining the right to single sex provision over the request for inclusion of transgender people of the opposite sex.
If someone has a GRC, they have to be treated as if they are of the opposite sex, so they have to be accepted into single sex provision for their claimed sex regardless of whether there is good reason to exclude them.
As there is only a relatively small number of people with a GRC, and they have gone through a gatekeeping process to confirm that they suffer from a condition whereby they would suffer from severe distress if they were to be treated as being of their natal sex, rather than preferred gender, their inclusion in single sex provisions of the opposite sex causes few problems.
If the GRA is amended to self identification, then the right to be treated as if one is of the opposite sex will not be limited to those who would otherwise suffer significant mental distress, and there will be no form of gatekeeping to ensure that someone is requesting to be so treated for genuine as opposed to nefarious reasons. The "good reason" provisions for maintaining single sex services under the Equality Act will be circumvented as the trans person will have to be treated as if they are of the opposite sex. There will be no way of drawing a distinction between a man wishing to be treated as if he were a woman because it causes him severe mental distress to be treated as a man, and a man who wishes to be treated as if he is a woman because it will allow him easy access to abuse women.