The mix-up led to the body of Philip Bradburn being cremated instead of that of Conservative MEP Philip Bradbourn.
A failure to provide written records created confusion between the two similar sounding surnames, the Heart of England NHS Trust said.
The trust and Central England Co-operative apologised for the blunder.
Former MEP Mr Bradbourn died at Good Hope Hospital, Sutton Coldfield on 20 December.
Mr Bradburn died at University Hospital Birmingham four days later and his body was sent to a funeral directors run by Central England Co-operative.
As Good Hope's mortuary was nearing capacity, a request was made by hospital staff to move four bodies - including Mr Bradbourn's - to the funeral company.
The names of those to be moved were given over the phone but not followed up with an email listing their names and addresses, the report found.
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The undertaker collected Mr Bradbourn's body, but four days later returned it to Good Hope, when his family requested to change his burial to a cremation.
Meanwhile, Mr Bradburn's body was sent back to the hospital over concerns it had been at the funeral directors for some time.
When it arrived at Good Hope from the funeral directors, paperwork carrying his surname was overwritten with the surname of the politician.
Doctors looked at these papers and signed off the cremation for Mr Bradbourn but the body of Mr Bradburn was released.
Central England Co-operative said: "Our priority has been to work closely with all concerned so that we can learn from this unfortunate incident and build further appropriate safeguards for the future."
Dr Andrew Catto, of Heart of England NHS Foundation Trust said there had been a "rare and complex set of circumstances".
He said: "We are very sorry that this incredibly distressing situation has happened."
Mortuary staff's failures to carry out adequate identity checks led to the wrong body being cremated at the funeral of an MEP, a report found.