There are a set of steps that need to be taken before the house can be transferred into your name. None of these could be done until probate is granted. You can ask what the steps are and how long each will take, and some like gathering the deeds, making sure there is no outstanding mortgage, will probably already be done. Local property tax, can be slow as you are dealing with the local council, and the solicitor may need a certificate from them before he transfers to you.
Your father and uncle will be able to give you a better idea of the specific next steps.