Utopia. Shangri-La.
The person elected to be President, with the power to over-ride what our elected representatives in Parliament decide, "chosen by us to referee the political process and champion the interests of the British people" will still need to be incorruptible and steadfastly non-partisan, with no bias toward his/her own popularity, power base, or chances of being re-elected.
They will need strong ethical views, but no political ones regarding which party is most likely to act in accordance with those views. They will need the memory of an elephant.
They will need to be recruited from those who have no ambition to take on the power that the position will give them, but nevertheless have the knowledge, experience and personality to carry it out without making enemies and the private fortune to rule out any temptation to follow policies which increase their own bank balance diectly or indirectly, or to accept favours from those they may have to discipline in the future.
Good luck finding a suitable candidate who is well-enough known to the public for them to vote for them, but isn't a show-biz celeb.