All wills since 1858 have been recorded in the National Probate Register. Indexes (calendars) are widely available in major libraries and record offices usually cover up to the 1940s. Local probate offices should have access to more recent events (past 50 years).
Use these to see if a will exists and other basic details (testator, date, executors, value of estate etc).
Once you are sure a will was made and proved (not all wills make it into the system and most people didn't leave wills) you can order a copy through HM Courts Service - see www.hmcourts-service.gov.uk/cms/1176.htm
If you can't get to a set of calendars you can order a search using their postal service.
If you can get to First Avenue House in High Holborn, London you can shorten the process immensely - they have the only publically accessible full set of calendars (1858 to very recent) and will get you a digital copy of any will in an hour or so for a fiver. Marvellous place!
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Currently researching: HEADs in west Berkshire (the Peasemore/Leckhampstead line). Newbury almshouses & many other aspects of the history of the area.