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His death shows that he was born in Wales and had been in Australia for 40 years.  You need to at least get the birth certificate of one of his children, preferably a birth that he registered himself, to see what is given as his place of birth.

Debra 

I have fixed the spelling, it is Ballygihen.

Debra 

It is possible that he had a short certificate from his original birth registration which would name him as Harold Arthur Forrest KOSELJ and he would simply tell whoever he presented it to that he was only known by the first three names.  He would be quite entitled to do that as a personal preference as long as he wasn't doing it to commit fraud.   This short certificate would not have parents' names on it though.

In another scenario, if they attempted to have a search done for an original birth registration but were unable to locate it, you would expect to see a late registration in the indexes in order for a birth certificate to be issued. There doesn't seem to be one.

Are you sure it was a birth certificate and not a certificate of baptism?

Debra 

..... he said it had an A in the top corner and after his birth certificate was lost in the post, he was informed by someone trying to help him get a copy, that an A meant he was adopted.

That person gave him bad advice.  If a child was adopted the original birth certificate would have the full word 'adopted' noted on it.  A new short form birth certificate would be issued and specifically had no mention of an adoption, just the name, date of birth and sex.  No parents were named.

Is anyone still alive who actually saw this certificate?  He wouldn't have needed a birth certificate to do most things, lots of people did not have one and a stat. dec. would suffice.

Debra 

Not much help here but some records.

Is this Peter?
Peter Heath, baptised 7th February 1819, Burton upon Trent -mother Sarah Heath

Banns of Marriage 1840 - Peter Heath and Eliza Atkin, Burton upon Trent
https://www.familysearch.org/ark:/61903/1:1:QL7D-5NSF

*i can’t see this marriage

He might have a brother baptised Allick in 1816 and named Alexander in 1841 at Burton Extra.  There are a lot of marriages that could be Sarah later on in the general area.

Debra