I would not take the approach outlined by Soontobe60. For example, the parent governor is not the appropriate person to speak to.
You've already cited the relevant guidance. As you've identified, with unisex provision, the privacy of the occupant needs to be ensured. It states that this will be achieved by, for example, having adequate enclosure and a full height door. It doesn't, and I think this is the problem you face, state that you must have a full height door. But the implication is that if a full height door is an example of meeting the requirement, all else being equal, the lack of a full height door does not meet the requirement and as such, your school is not compliant.
Note further, unlike as some people claim, there are not prescribed ratios, nor does there have to be a wash basin in the cubicle.
So what should you do?
First, email the head teacher and CC the school's safeguarding officer. Cite the regulations and explain how the facilities do not meet them. It could be (just possibly) that there is some other facility available that you don't know about, in which case they can tell you about it. It's up to you, but I honestly think you'll get a better response by taking the emotion out of it. Don't get into why it matters, the sensibilities of your child, or even, at this stage, the safeguarding risks. Just state that the regulations are not being followed and you want it changed.
If you've already done that, or if the headteacher replies with an answer that isn't satisfactory to you, write to the clerk of the governing body of the school, CCing the chair of governors, saying you wish to raise a formal complaint about the headteacher's response to your issue. They are obliged to investigate it. Check the school's website for their complaints policy which will explain how the complaint will be handled. If the governors' response doesn't satisfy you then you are entitled to appeal (still within the school). Most likely the appeal will get the same result, but it's important to follow the process. You can then appeal externally, but likely you'll only succeed if the internal appeals process was not followed correctly.
At any point, but certainly if the appeals fail, you can also file a complaint with OFSTED, and with the Local Authority (most have a MASH - multi agency safeguarding hub), citing the safeguarding risks of continued disregard of the regulations
If you still don't get satisfaction, try the Local Authority more broadly, your local MP and/or the local press.
Do keep in mind that most schools wouldn't choose to be foul of the regulations and clearly they do need to follow them. But most schools are also very short on money, and changing their facilities is an expensive business. So even if the will is there to make the change, it's not trivial and I wouldn't expect it to be an easy process. It doesn't mean it shouldn't be done of course, I'm just saying that the resistance might not come from a place of contempt for your viewpoint.
Hope this helps. Good luck.