I'm sure I'm not alone in having nearly all of those , and many more. The only one I don't care much for, and even less for the author, is Falkus. I found his books hectoring and dogmatic and anecdotes from friends who'd met him didn't help my estimation of the man . Of living authors, Gierach is pre-eminent , and I think Trout Bum is one of the best written, and certainly the most entertaining book ever written on the sport. I write myself , and reading Gierach can make me weep with sheer envy sometimes .
Lord Grey of Fallodon, Plunket Greene and Haigh Brown are all magnificent, if from a very different era , and I think it is a great shame that Chris Yates confines himself to coarse angling (which I practise , but not exclusively) as he writes from the heart , and in an exquisite style .
Best known for their other work , of course , but Arthur Ransome and Hemingway are both every bit as good as one would expect. I will also mention one little known gem , and that is Thy Rod and Thy Creel by Odell Shepherd, which is essentially about the philosophy of our sport .
Again , not fly fishing , but Somewhere Down the Crazy River, by Paul Boote and Jeremy Wade(a long time before he was that bloke off the telly ) is a wonderful read . I have just discovered that even my paperback is worth 100 quid plus now.