Search here:
https://www.gov.uk/search-will-probate
As the death occurred before 1990, the search will apparently show that no records have been found. However, underneath that information, there should be a link where clicking on it brings up a copy of the index sheet on which the death is recorded.
Alongside the image of the index, there should then be a form which you can copy the info from the image into. Submitting that form will order a copy of the grant of probate (including the will) for you.
You won't be able to download the document immediately though. Someone will have to locate the original document, scan it and then upload it to the web in order that you can then download it.
Once that's happened, you should be sent an email to tell you that the document is ready for you to download. If you don't receive the email after a few days though, log into your account to see if the download link has become available.