As far as I know, the ownership of a sword is not acctualy illegal. There are rules on some preventing their purchase, but if you allready have it it's legal. Carrying one outside is a different question, But if the pictures where taken inside the owners home there is nothing stopping it (that I'm aware of).
A simmilar situation exists with flick knives, and telescopic batons. both are legal to own, but maynot be sold, lent, hired, bought, imported or produced. It would also be illegal to carry one.
The second article mentions pictures of them with alcohol, which could lead to prosecution (under 16's maynot drink alcohol except in thier own home, under parental supervision. and between 16 and 18 alcohol may only be drunk with a meal, and only beer, wine or simmilar (as I understand it, never had confirmation on that bit))
Probably turn out to be "behaviour likely to breach the public peace" or "behaviour likely to incite violence"