Which is fair enough but then can you argue that he, the executor, is doing the work when he stands to gain from the will but only if he executes the will by instructing someone else?
I don't understand what you are saying here.
Whether an executor is a beneficiary of a will or not they can get a solicitor to do most of the work. The solicitors costs are paid out of the estate. If the will states that they get say £1000 for acting as executor and they get a solicitor to do most of the work, yes, that seems a bit against the grain but that is how it works.
Solicitors have special bank accounts which are 'client' accounts so they don't have to open a bank account in the name of the estate which an executor would have to do so some things are simpler and quicker. (These accounts are regulated by the law society and audited by independent auditors annually).
A solicitor also knows how things work so it might well speed the process up rather then an executor who isn't sure what he is doing.
Given P is the appointed executor you do need to work with him - and if he gets a solicitor to do the majority of the work - you need to come to amicable arrangements on things, as it is the executors duty to arrange valuations for both probate and sale, and dispose of the contents of the property as they see fit, so you want to stay on good terms if you want to be involved in the process.