It would appear from reading that Twitter thread that the club's action will be for breach of copyright in that the club allege he has been supplying copies of Swans shirts in breach of their copyright, Rob is presumably claiming that they were not copies but original shirts bought from official sources that he owned and was selling as used/second hand shirts.
In normal cases of breach of copyright the copyright holder would usually have obtained evidence by way of test purchasing shirts from the alleged culprit or had complaints from purchasers that they were not original bone fide shirts. Any online posts on forums, facebook, twitter etc is incredibly easy to find and recover as evidence to show that items were being offered for sale, bank accounts will show payments from Paypal etc(which include a description of the goods).
If convicted of this offence, i would imagine that the club would make an application under the Proceeds of Crime Act which would seek to recover any benefit made from that breach of copyright. Any profit any culprit has has made will be recovered from any assets such as their home, car savings etc.
Breach of copyright is regularly prosecuted by Trading Stndards dept of your local authority.