I concur with the advice to use the Group Travel for whichever InterCity operator you want to book with. I've done this for a couple of choir trips, and they've been really good at managing the best value between Group Fares and various permutations of Railcards.
However, be careful if your journey involves multiple TOCs. One booking I did was Grantham to Cambridge with a return break of journey at Ely (so LNER/EMR/XC/Anglian/GTR all potentially involved depending on which train(s) were used), and that got quite fraught until I found someone really clued up to talk to. My experience was that the team at LNER were really good, and had the experience to make something a bit out of the ordinary work, but that I had to talk to them, not just email.