First thing, you need to see the Will. If the property was in the husband's sole name then chances are it is going through probate as that will end up being needed.
If it is not on the gov.uk website give the probate registry a ring and see if they can check in case it is missing by accident. If not, check with the person who was the Executor and ask where she got her copy from. If a legal secretary made it, then there is a chance if they don't have the original at home that the secretary took it back to their office and that firm has it.
Without seeing it, it is just a best guess, but I expect that the Will has left the property in trust with a life interest to the spouse and then to you on her death.
That would mean that until the spouse dies, the property is the responsibility of the Executors/spouse. If the Executor has decided not to be the Executor, someone will end up getting appointed so you need to find out who is doing it (has she left it with a solicitor?).
The Will will say who has the responsibility for maintenance, but it is unlikely to be you. The Will is likely to either give the life interest to the spouse on the basis that she pays all outgoings and maintains the property or the Will will provide for the Executors to insure and maintain the property from the estate (so out of the deceased's other money). The first tends to me more common, but unless you are the Executor you are unlikely to have any responsibility until the spouse dies.
Unless you have been appointed as an Executor/Trustee you are what is known as a 'remainderman', so you get the remainder once the life tenant dies and although you will get something eventually, you do not have any interest or a liability at this point.
As far as the household bills and Council tax are concerned, they will be down to the spouse as the occupier. If the property were empty, they would be the responsbility of the estate. Buildings insurance could be either the estate or the spouse depending on what the Will says.
Hope that helps.