As a teacher of ESL, I don't consider that sentence would confuse or mislead any woman (or man) with limited English.
As an ESL speaker who is also in contact with many other ESL speakers, I know that this sentence is confusing and misleading. And I know many ESL teachers are concerned that the imposed changes in language arising from this ideology are confusing for their pupils, so I have my doubts your assessment is an accurate reflection of your pupils' understanding.
The only context in which I knew about health issues related to anything "cervical" was spinal injuries and illnesses. Like the one my aunt suffered from.
I only learned about the word cervix when I was pregnant and the midwife explained what happens to the neck of the womb when you go into labour.
Yes, that is the word for cervix in my language - neck of the womb. That's what I thought the word was in English. That's also how the midwife explained what the cervix was - the neck of the womb.
And my English skills at this point were already near native level. Yet I still did not know the word cervix.
But we don't even have to restrict ourselves to ESL speakers. Almost half of all women do not know what a cervix is. Various surveys have all returned the same result.
ESL speakers do not make up that large a group. There are many many native speakers of English who do not know that word and who would not know that this sentence
"Each year, more than 3,200 people are diagnosed with cervical cancer in the UK."
refers to a cancer of the female reproductive system, that is, a cancer that only women can have.
Any health campaign using language that almost half of the target audience cannot understand is an embarrassing, abject failure in health communication. According to a friend of mine whose job includes writing health campaigns, this is an unacceptable, wholly misguided deviation from accepted practice and above all it's negligence that will cost lives. Real lives.
Given the recently publicised scandal in Scotland caused by miscommunication about cervical cancer in one particular patient group, I can only hope that at least NHS Scotland will rethink its approach to cervical cancer communications and speak to women about women.