High blood pressure will not increase the urine frequency, but yes, the BP medications such as water pills or diuretics can. Not all BP medications increase urine frequency, so ask your doctor if your medication is causing increased frequency.
Other causes of increased frequency are diabetes mellitus, (high blood sugar), diabetes insipidus, urinary tract infection and prostate enlargement (in males).
Please discuss with your doctor. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.