It doesn't mention criminality, it just says they have been identified as undesirable and will be refused admission to the Amex (which, as a private place, the club are entitled to do).
I reckon they've not given you the whole picture. Generally speaking police can only arrest someone if they've committed, or to prevent, an arrestable offence (which they can't have done as the threat is for the future) or if they are in breach of of an order or bail condition.