If you are personally handling the winding up of a deceased's person's affairs as their executor then you can now apply online for the grant of probate (see https://www.gov.uk/wills-probate-inheritance/applying-for-a-grant-of-representation). The online trial which I previously reported on (see http://www.breakinglaw.co.uk/search/label/probate) has just been extended. You should find the process relatively straightforward. This applies where the deceased lived in England and Wales. But the online system will not presently cover applications for a grant of letters of administration which is the law's answer to probate where the deceased did not leave a will. For who gets what with no will and who can claim if they have been left out under the will or the intestacy laws which are triggered by no will, see that excellent book Breaking Law by 'erm - me!
Fees for applying for probate are set to be increased next April so don't hang about in making a probate application. Most certainly, don't kill anyone off to save on fees.