If you are the executor and the estate of the deceased is straightforwrd, there is no reason to have to use a solicitor - and certainty not solely for the reason of solving the 'immediate costs' issue - for which the above is good advice.
The house of the deceased cannot be sold before probate is granted, but marketing can commerce.
But as kinell pointed out, probate does not take too long to apply for / grant if the executor gets organised and prepares the forms.