While on Effexor, I developed high blood pressure, for which my primary did nothing except chide me to increase exercise (like it didn't matter that I taught 6 classes daily of secondary school while STANDING and circulating around the large room was not exercise, along with early morning brisk walk AND coming home to attend to my family and elderly mom!). It was her PA who became distressed at my high readings one day when my primary was not in. I had gone in due to excruciating leg pain, and she saw that I was on Effexor, and informed me that the drug is known to affect serious BP issues. Unfortunately, her solution was to take me off the Effexor and immediately start on Paxil. NOT a great idea! Meant abruptly discontinuing the Effexor. I did my homework and obtained reliably sourced info advising strongly against that, so I just continued with that drug rather than create more issues for myself. Besides, I had been for a very short time on Paxil years before and it affected me with its own set of side effects so I was not interested in returning to those. To this day, I have HBP and presently take two medications in efforts to tamper it to within my cardiologist's acceptable parameters. Life circumstances and present health concerns create valleys withe the readings. My comments are meant to advise you that there is yet another nasty side to Effexor...

In regards to what you go through in the UK in order to see your doctor(s), it does seem that the situation is more dire than what happens here. Here also there can be long wait-time on the phone, but we do have something called Call Back in which you can tell the automated recording that you want them to Call You Back. And oftentimes they do! Other times, no call. I live within a 4 minute drive to my primary doctor so I will go there in person, just as you propose to do! I will go with a letter detailing the reason(s) for needing her attention, and won't leave until her nurse comes to the front desk to personally take it to her. You do what you gotta do! I'm so sorry that you appear to have much more stress in dealing with your medical professionals. Personally, I find all of this disgraceful and unacceptable but I don't place blame on the doctors, it's the institutions that regulate how much time they can actually give each patient during an office visit, etc. Here, I have 2 doctors who are allocated NO MORE than 10 to 15 minutes per patient!! There are consequences from what an investigative reporter has discovered with his informants. On Thursday, I had an appointment with one of those doctors, and I had a great deal to get across regarding serious developments with my conditions. I found myself speaking faster and faster as I noticed her furtively glancing at her wrist watch. And my annoyance and aggravation came across in my tone. I finally told her "Here," as I handed her a 2 page print out that I had comprised, "you can learn more from what I've comprised for you since you don't appear to have enough time to attend to my concerns." She did blush, apologized and thanked me for the info which she said she would indeed read and include within her summary. I left that day with my heart racing, and the nurse had taken my pressure and it was high BEFORE the visit so I can only imagine what it read afterwards.

May I suggest that you keep a journal of sorts, detailing your experiences while tapering off Effexor (and equally valuable for other medical info and meds).
Best of luck to you. I would appreciate hearing from you and how things go for you.