Archer has been found to be a liar and fraud on more than one occasion, but I think the main reason people dislike him so much is his unbearable smug, supercilious manner. A face in need of a slap if ever there was one.
The Daily Mail is guilty of the most ridiculous knee-kerk right-wing reactions to just about anything. I'm no fan of Tony Blair but I'm sometimes amazed at just how many things they think they can blame him for - Hurricane Katrina, Arsenal being knocked out of the Champions' League, Sudoku being too difficult etc. OK I'm exaggerating, but not by much. The blustering outrage of "journalists" like Peter Hitler and Simon Himmler...oops sorry, force of habit...Peter Hitchens and Simon Heffer can be quite amusing as long as you don't take it seriously.
As for Thatcher - she's loved and hated in equal measure really, so it depends on your view. She was either the greatest leader since Churchill, or an overbearing, belligerent warmonger. She was either strong, determined and knew her own mind, or was stubborn and refused to listen to anyone. She either "freed the working classes" (one of the aforementioned Heffer's most hilarious comedy moments) or she left hundreds of thousands of people with no jobs (perhaps that's what Heffer meant), no sense of self-worth and seemingly no future. Ya pays yer money, ya takes yer choice.