No. Because the Codes were written in specific reference to the Equality Act 2010, which does not require somebody to have a GRC to have the protected characteristic of Gender Reassignment. Interestingly enough, the Statutory Codes use the phrases "according to the gender role in which they present" and "acquired gender" synonymously and interchangeably within the same relevant segments when referring to anyone with a s7 characteristic. I just use "acquired gender" in my posts because it's a sum total of two words, as opposed to nine.
I disagree although it's possible we're talking at cross purposes. As my posts above indicate there are subtle differences in the application of the Equality Act depending on whether you have a GRC or not. Further, my view is that the majority of the references in the EHRC codes to transexuals are intended to refer to people who have been through the process and got a GRC (the Govt's expectation was originally that most trans people would do this). There are some references to treating people in the gender in which they present, which would have been intended to include those going through the process of living in the opposite gender prior to obtaining a GRC, but it's important to note those references are often qualified.
Let's take the service provision guidance as that is what the OP was asking about.
www.equalityhumanrights.com/sites/default/files/servicescode_0.pdf
13.57
If a service provider provides single- or separate sex services for women and men, or provides services differently to women and men, they should treat transsexual people according to the gender role in which they present...
13.59
Service providers should be aware that where a transsexual person is visually and for all practical purposes indistinguishable from a non-transsexual person of that gender, they should normally be treated according to their acquired gender, unless there are strong reasons to the contrary.
Points that I think are important to note are:
A) The paras above are written on the assumption that the service provider provides for both sexes with no gender neutral provision. It does not consider situations where there may be a gender neutral option in addition to single sex services. It's worth noting that eg the EHRC guidance for schools does approve of private gender neutral spaces being offered to trans pupils when changing for PE. So I wouldn't take the above paras as evidence that third spaces are never an option.
B) Whilst both of the above paras are framed in a positive way, the obvious implication from para 13.59 is that if a transwoman is clearly distinguishable from biological women then it may be appropriate to treat them differently. The obvious example as in my posts above is a transwoman who has not had surgery in a communal changing room. A more subtle example would be someone who looks very much like a man (eg because they are just beginning their transition) wanting to use the female changing rooms in a clothes shop. IMO, if there is a private gender neutral space it then it may not be a breach of the Act to ask them to use it.
As mentioned in my post above though, whilst I think the GRC could be relevant to whether a person is likely to be able to successfully sue a service provider if they have been excluded from a single sex space and offered a gender neutral space instead, in reality this probably won't inform any shops' transgender policies etc. because it isn't obvious who has a GRC and who does not. The guidance above does say that service providers can ask to see a birth certificate where they need to know someone's legal gender (para 2.27) but this obviously isn't something which people are going to ask to see in order to access the changing rooms at a clothes shop.