TC has largely answered your question, Jennyjoan, but I'll add in a bit from my own personal experience:
When my father died in hospital, the first thing I did (after visiting his sister's house to pass on the news and then registering his death at the Register Office) was to go round to his house and find his will. As I'd largely expected, it named my as both sole executor and as sole beneficiary.
Over the next few days I first visited the District Probate Office to pick up the form to apply for probate (and to get some advice about the formalities) and then started on collecting as much of the relevant information as possible (such as details of his pensions, bank accounts and tax position) that I could get hold of without yet having probate. Within a very short space of time, I'd completed the form, submitted it, attended to probate office to swear an oath (or, more accurately, to 'affirm' because I'm an atheist) and been granted probate.
My father died around mid-to-late October (I'm lousy at remembering exact dates!). By the end of November I'd completed the whole process, transferred my father's money to my own bank account and bought a nice car out of the money too.
(As TC has said, the will automatically moved into the public domain as soon as probate was granted).
So things can move at quite a pace when everything is straightforward and the executor really wants to get on with things. However an inefficient executor, together possibly with a few complications in the will or with the estate, can see things dragging on for years!