'IHT' is Inheritance Tax. You won't need to bother about it if your father's estate is worth less than £325,000. (If your mother pre-deceased your father, leaving everything to him, that figure goes up to £650,000). From what you've written, it seems that it won't affect you anyway.
You normally need to seek probate on a will (by applying to the Probate Registry) before you can start to distribute the assets of an estate. (There can be exceptions where the value of an estate is very low though). It's a very simple process, usually involving nothing more than collecting some information together, filling out a form and swearing an oath (or 'affirming' if, like me, you're a non-believer). The people at the Probate Registry are very helpful and you definitely DON'T need a solicitor to do the job.
Once you've received the 'grant of representation' (= 'probate') you're trusted by the Probate Court to distribute the estate in accordance with the will. Nobody has to approve any part of what you do but anyone who wishes to challenge your decisions can apply to the Court to do so. Again, you do NOT need a solicitor!