My sympathies on your loss.
No, he can not just take over unless it is mentioned specifically in the will that he is the executor of your fathers estate. If he did, then you are stuck with him. Your father should have stated in his will who he wants the executor/administrator of his estate to be. That is the person who will administer the estate and apply for a grant of probate. If he listed this solicitor (or any other one) to be the executor, then no, you can not do it yourself, you have to use that solicitor. He could renounce his rights to be the executor, but why should he? It is how he earns his living, and he would also want to respect the wishes of your father, and make sure his estate was dispensed with according with his wishes.
If the solicitor who is merely holding a copy of the will is saying that he was not listed as executor, then I guess you'll find out who it is when the will is read. Perhaps your father nominated another family member or a different solicitor to be the executor of his estate? If the solicitor holding the will is not the executor, all he does is hand it over to you. You do not have to have anything more to do with him unless you choose to. Drawing up a will for a client, and keeping a copy of it for the next of kin is not the same thing as being the executor of the estate once the client dies. They are 2 totally separate things, unless the person writing the will specifically says that he/she wants the solicitor to be the executor of his estate.