Alpha Telecom has 5p/min for 0844 and 10p/min for 0871, about their only good rates

With the greatest of respect to the Original Poster (I will avoid the term OP which could clearly be seen as an obscure form of forum abbreviation) it is this old fashioned deference to doctors as people who we do not like to upset (as though are like our schoolteacher or headmaster or something) that leads them to have the nerve to try to get away with switching to these covert premium rate numbers to ramp up the income of their surgery.  In view of the massive practical difficulties the use of this 0844 is causing in your case you really should complain to your parents' MP as MPs are now very concerned about the misuse of these numbers by GPs and the NHS is looking to gather evidence from MPs who have practical examples of constituents suffering real harm.

I know how you feel about not interfering with your parents affairs with their GP as they become older and more infirm but having just been through that dilemma following my 73 year old mother's hip replacement operation I have come to the conclusion that it is inevitable that one must interfere as one's parents get older and less able to stick up for themselves, just in the same way that they had to do everything for you when you were 5 years old.  My mother had her recent hip replacement privately after her NHS doctor had delayed it for over 2 years by denying there was a hip problem and eventually she could not walk at all and was reducing to crawling up the stairs on her hands and knees.  Then after she had to have the operation privately on her medical insurance to avoid a 12 month wait the NHS GP tried to deny her ongoing prescription drugs and essential physiotherapy on the NHS when she returned home by taking the ridiculous line that if she had private medical insurance she was now expected to pay for everything connected with recovering from the hip operation even when out of hospital.  However he reality was that my mother's private medical insurance, like that of many people, only covered her for in patient treatment and even then that was subject to her paying the first £2,500 of claims each year.

So coming back to try to help you what I learned in my mother's case that may help you is that the PCT (Primary Care Trust) responsible for your parents GP surgery will accept anonymous complaints about problems anyone has had dealing with a GP surgery and that they actively encourage such anonymous complaints precisely because they know that they may not otherwise get useful information about poor GP practices because of the old fashioned feelings of deference that most British people generally have towards their doctors.

GPs are jolly well paid professionals who are little more than glorified and very well paid social workers with a medical training and it is quite ridiculous that when a well paid doctor fails to deliver their service adequately (and that failure includes the primary means of communication) that people feel embarrassed about complaining about it.  In my mother's case I found that although she was initially nominally opposed to the idea of my intervening after I did so anyway and spoke to the practice manager to challenge drugs not being provided on the NHS and they then gave in she in fact approved of what I had done as she had been furious about the doctor's attitude and trying to deny her drugs and physiotherapy treatement on the NHS once she was back home.

I agree relationships with parents can be difficult but I think you are being too embarrassed about all this and you should register an anonymous complaint with the PCT (they will have a website which should be linked from the website of the doctors surgery ) If you do also complain to the doctor's surgery directly they are not going to pick up the phone to your parents as it was perfectly obvious to me that they are quite used to children taking up the cudgels for their elderly parents when their parents increasing  infirmity leaves them lacking the energy or faculties to do so properly on their own behalf.

At the least complain anonymously to the PCT and also ideally to at least your own MP (if you are still on the electoral register as an expat somewhere in the UK) as an example of how these numbers are now doing real harm to patient relationships.  Also your own MP is not going to contact your parents about this but he may use the information to add to the clamour of MPs demanding that the use of these immoral numbers by unscrupulous GP practices be bought to an end.