Comparisons have a bad rep. Reading Villette, I'm reminded of an early review of Look at Me: 'a novel sufficiently distinguished to make you blink twice at "Brookner". Blinked at once, it might be "Bronte".' Other early comparisons included Muriel Spark, Barbara Pym, Elizabeth Bowen, Virginia Woolf, Edith Wharton and of course Jane Austen - whom Brookner excoriates on more than one occasion.
Comparisons with male novelists - Henry James, especially - come a little later. Later still - into the new century - we see references to the great Europeans. '[Brookner's] characters, reflective, displaced and intransigent, are more like those of Camus than of any contemporary British novelist. Her style has a similar purity. Increasingly, Brookner reveals herself as a European novelist, and a major one,' wrote Helen Dunmore of The Bay of Angels (2001), a judgement she repeated in her 2010 Introduction to Latecomers (Link): 'Anita Brookner is the most European of British novelists'.
One wonders what Brookner would have made of the Brexit vote.
(But Brookner's politics are never explicit. I can remember her once mentioning Conservative Prime Minister John Major in the 1990s, when, in an aside, she defended his misunderstood 'back to basics' policy. Otherwise we're in the dark. But working out the political leanings of great novelists is an enjoyable parlour game. We know that Trollope stood as a Liberal; nowadays we would probably call him a One Nation Conservative. James was right-of-centre too, but Dickens on the left. And Brookner? I would risk a suggestion that she probably voted Tory. But with Brookner you can never be sure.)