How do I go about verifying birth & death details in England for an individual who lived and died in the 20th century?
As starting points I have a name of the deceased individual and his place of origin is assumed to be in England.
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For somebody (believed) born in England or Wales in the 20th century, the first point of reference is the GRO (General Register Office) Indices of Births, Marriages and Deaths (BMDs).
These can be searched online at a number of subscription websites but FreeBMD is free and has good coverage of births up to the early 60s and deaths up to the early 70s. (If the events you are interested in are later than these dates, you may need to pay to access a subscription site).
There's also a plethora of links at FreeBMD's civil registration information pages to help you understand what you're dealing with, but in essence:
If you can name the assumed place of origin, I may be able to refine this answer. A few (not every) local Registrar's Office have allowed their records to be indexed on line. If the area you're interested in has done so. You can look at UkBMD to point you in the right direction.
(Scotland and Northern Ireland will have different answers, which I hope somebody will come along to give for completeness).