Absolutely not. The law was written so that trans women could be excluded from women's spaces if it's legitimate and proportionate.
The statutory guideance says:
f 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. However, the Act does permit the service provider to provide a different service or exclude a person from the service who is proposing to undergo, is undergoing or who has undergone gender reassignment. This will only be lawful where the exclusion is a proportionate means of achieving a legitimate aim.
The gender critical organisation Fair Play for Women acknowledges this, too.
https://fairplayforwomen.com/equality-act-2010_womens-rights/
3.60 Any exception to the prohibition of discrimination must be applied as restrictively as possible and the denial of a service to a transsexual person should only occur in exceptional circumstances. A service provider can have a policy on provision of the service to transsexual users but should apply this policy on a case-by-case basis in order to determine whether the exclusion of a transsexual person is proportionate in the individual circumstances. Service providers will need to balance the need of the transsexual person for the service and the detriment to them if they are denied access, against the needs of other service users and any detriment that may affect them if the transsexual person has access to the service. To do this will often require discussion with service users (maintaining confidentiality for the transsexual service user). Care should be taken in each case to avoid a decision based on ignorance or prejudice. Also,the provider will need to show that a less discriminatory way to achieve the objective was not available.