Don't worry, your solicitor will sort all this out for you.
You will need to provide all the relevant documentation to your solicitor ie copy death certificate (if joint tenants and his half automatically passed to you on his death) or probate/letters of administration (if you were tenants in common).
Provided that you have the right to sell the house yourself (ie now own it all yourself) and you can provide the necessary documentation then there will be no problem.
Copies of the documents will be sent to the buyer's solicitor who will then send them to the Land Registry after completion for the property to be registered in the new buyer's name. The solicitors will not let this happen unless all is in order and the Land Registry will sort all the change of name out.
Provided all the documentation is available there will be no delay.
As regards the deeds, when did you buy the property and do you know if it is registered at the Land Registry?
Your deeds may be with a mortgage lender, the solicitors who acted for you when you purchased the property or may have been sent to you. It may be a good idea to make sure you know where they are, especially if the property is not registered at the Land Registry.
Also make sure you have copies of things like guarantees or warranties and details and documentation relating to any work done as these are likely to be asked for by a buyer's solicitors.