I think that the Lasting Power of Attorney process is indeed one that one could do on one's own, as Daylily has said, and thereby save any solicitor's fees.
However, there is a general point I want to make here: not all legal processes can be carried out by amateurs; the law is a complex field of knowledge. I would therefore advise everybody to find a solicitor that they can trust and feel comfortable with, because sooner or later, most of us need professional legal input in dealing with something that requires expert knowledge.
We don't have to pay our doctors or dentists upfront, as we do our lawyers, and we all self-medicate for minor problems, but we still all accept the absolute need for professional medical help from time to time, and we therefore try to find practitioners who have been recommended to us by others, whom we like and get on with as people, and whom we can trust as experts in their field.
I suggest the same is true of the legal profession. Lawyers are not all money-grubbing scam artists, any more than all doctors are quacks...
I have found my own solicitor not only competent and helpful over the last 10 years, but more than that: he has been a reassuring friend in dealing with everything from my late parents' estate to my LPA for my husband, and recent changes to my Will. He is technically retired now, but I have moved on to a younger partner in his firm, and even though this means I have to travel from London to Cardiff to see her, it is worth it, in my opinion. (I also like to have an excuse to go to Cardiff sometimes...) Just picking a solicitor out of the phone book is no different from picking a doctor or dentist that way. You need recommendations and personal experience.