Well he COULD be [wrongly] prosecuted (and quite possibly convicted for) criminal damage to the door ad/or burglary (which only requires 'breaking and entering' to take place, even if nothing is taken). Such a prosecution would be based upon DNA evidence from his blood and the false assumption that he had broken into the property.
However if you're simply asking whether he's actually committed any offence, the answer is 'No'. Anyone can lawfully enter another person's property if they don't need to force entry to do so; trespass is only a civil matter, not a criminal one. (There are certain exceptions to that, such as a trespass on railway property, but they're not relevant here).
John certainly hasn't committed theft, since the definition of theft is thus:
"A person is guilty of theft if he dishonestly appropriates property belonging to another with the intention of permanently depriving the other of it".
The appropriation of the bag is not 'dishonest' because the law states:
"A person’s appropriation of property belonging to another is not to be regarded as dishonest—
(a)if he appropriates the property in the belief that he has in law the right to deprive the other of it, on behalf of himself or of a third person"
Further, the property is not "belonging to another".
http://www.legislatio...g/definition-of-theft
Chris