It's one of the most controversial strips 2000 AD ever ran. Yes, even more than Big Dave's other stories. It's having a go at the royal family, in particular portraying the Princess of Wales and the Duchess of York as drunken, trashy slappers who'll try to pay a taxi driver with sexual favours instead of cash. This is funny and the story's good. But, yes, people got upset.
Rereading it, it's notable mostly for returning you to the days when Princess Diana and Elizabeth the Queen Mother were still alive. The bit of the story that's actually offensive is the brief caricature of Japanese tourists and their wrong, wrong, wrong dialogue. "Banzai! Hahaha! Kamikaze!" "Tora! Tora! Tora! Hirohito!" It's quite possible that Japanese readers wouldn't see the humour in that, c.f. the offence that was caused by Have I Got News For You many years ago with a quiz question about Hiroshima and Nagasaki that to British eyes would look completely innocuous. But never mind. It's completely correct and in-character for Big Dave.
Also, Big Dave's extremely unfortunate postman is the children's character Postman Pat. Dave's pit bulls eat Pat's cat, then Dave flushes the letters in Pat's sack down the toilet while holding Pat's head in the (just-used) bowl.
The plot involves Dave's search for his giro cheque. He doesn't work, obviously, so he wants his thirty-six quid. Offer him that and he'll do any disgusting deed you care to name. The baddies are ostensibly Diana and Fergie, who've kidnapped the royal family and replaced them with robot duplicates, but unfortunately Dave isn't very clever.
PRINCE CHARLES (real): drawn superbly by Parkhouse.
PRINCE CHARLES (robot): looks like Bill and Ben, the Flowerpot Men. "Don't. Listen. To. Him. Dave. It's. A. VZZZK! Trick!"
Dave can't tell the difference and ends up machine-gunning the royal family. Because he's an idiot. He then shags two cheap trollops (i.e. Diana and Fergie), then slaughters the British Army. While his dogs eat another of Postman Pat's cats.