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.
Updates on this story and more from Birmingham and the Black Country
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."

They also rejected a plan to introduce free parking for the first 30 minutes.
The changes were proposed by four DUP MLAs, but Infrastructure Minister Chris Hazzard said their motion was based on "seriously misguided logic".
He added that enforcing the 30-minute free parking system would be "extremely resource intensive".
However, the assembly did pass a Sinn Féin amendment calling for a review of on-street parking arrangements which Mr Hazzard said he was "minded" to implement.
"I'm certainly not opposed to a review of sorts - a strategic review of on-street car parking policy and the direction of travel," the minister told BBC News NI.
"What I was opposed to, with the DUP motion, was their pre-determined outcome of any such review, that we would set in stone before we began a massive reduction in penalty fines, I don't think that would be appropriate."
The rejected DUP motion was signed by ex-minister Edwin  Poots, and his party colleagues William Humphrey, George Robinson and Alex Easton.
They said "greater flexibility" was needed in parking policy to encourage more trade in town and villages.
Parking enforcement in Northern Ireland was privatised in 2006.
Initially, fines were levied at £60, with the option of a 50% reduction if the bill was paid within a fortnight.
However, in 2012, Stormont MLAs voted for the penalty to be increased to its current level of £90 - or £45 if it is settled within 14 days.
The then Roads Minister Danny Kennedy said at the time that bigger fines would "act as a greater deterrent to those who choose not to park properly".
The current minister said "at least two thirds" of people who receive parking tickets pay within two weeks, and therefore pay at the lower rate of £45.
"I think, when we look across many states, this is an appropriate amount, "Mr Hazzard added.
Last month, a Belfast City Council committee voted to end the council's annual policy of offering free car parking in the city centre in the run-up to Christmas.
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.
[NEXT_CONCEPT]
MLAs have voted against DUP calls for a significant reduction in the £90 mandatory parking fine during a debate in the Northern Ireland Assembly.