As I read it, there's not a total prohibition on taking cyclizine if you've got high blood pressure; it just requires the approval of a doctor or pharmacist first:
https://www.nhs.uk/medicines/cyclizine/who-can-and-cannot-take-cyclizine/
I would assume that the prescribing doctor has already performed that function. If in doubt though, I suggest consulting a pharmacist. Our local hospital has a dedicated helpline for such enquiries
(
https://www.esneft.nhs.uk/service/pharmacy/medicine-advice/ ).
It's likely that your own hospital will offer a similar service, so why not give them a call for peace of mind?