It’s easy to see why Julia is drawn to Rex. He’s a bit older and more mature than the boys she’s dated, he’s well-off, he’s mysterious, politically connected, lavishes her with ornate gifts, and drives her around everywhere she wants to go. She gets to treat him with both possession and disdain and he still worships at her feet. And then there’s the icing on the cake – her mother doesn’t like him. Talk about the perfect guy!
But even before Julia knows the real Rex, as readers we suspect that something’s up. Waugh is careful not to let us like this guy too much. First of all, he’s irritating. He’s that super-capable but obnoxiously-loud guy who will bail you out of jail in the middle of the night but "rejoice in his efficiency" while doing so. Even Charles feels that "in his kindest moments Rex display[s] a kind of hectoring zeal as if he were thrusting a vacuum cleaner on an unwilling housewife." Rex also seems to have no shame about carrying on an affair with the married socialite Brenda Champion, even while he’s wooing Julia. He also treats his potential marriage as a business arrangement. As Charles says of Rex, "He wanted a woman; he wanted the best on the market, and he wanted her cheap; that was what it amounted to."
And it’s all downhill after the engagement. Rex treats Julia’s religion without respect, converting without thought or effort and trying to replace sincerity with money ("All right then, I'll get an annulment. What does it cost? Who do I get it from? Has Father Mowbray got one?"). We hear the tragic tale of their marriage only years after the wedding (which Julia calls a "gruesome affair" in itself). As she explains, Rex started up again with Brenda Champion only months after their honeymoon. Charles notes that his political welfare has gone downhill considerably, too, as he made some questionable friends, "flirt[ed] with communists and fascists," and was all around a "vaguely suspect" character.
But most disconcerting is Julia’s repeated claim that "Rex isn’t anybody at all. […] He just doesn’t exist." In a way, Rex suffers from the same lack of people skills that so define Julia’s brother Brideshead (see his "Character Analysis" for more). He has "the faculties of a man highly developed," as Julia says, but he doesn’t understand human emotions. This explains why he is able to treat proposing to Julia as a business arrangement, why he doesn’t care that their baby was born dead simply because she was a daughter and not a son, why he doesn’t understand why his wife is upset at his affair with Brenda, and why he seems to not really care that his wife is cheating on him. He’s not even angry with Charles for the affair! All he says is, "If I've been around too much, just tell me, I shan't mind." Even when Julia is readying to divorce him, Rex is concerned with politics, not love. With casual annoyance he tells Charles that "there's too much going on altogether at the moment […] and I've got a lot on my mind. […] If Julia insists on a divorce, I suppose she must have it. […] But she couldn't have chosen a worse time. Tell her to hang on a bit, Charles, there's a good fellow." It looks like Julia’s assessment is largely correct: "Rex isn’t a real person at all."