Given that Brian Eley is never realistically going to return to competitive chess I think there is a case for removing him from any list of eligible players and if the ECF needs to give a reason then they could say that it was for bringing the game into disrepute. Granted he has never been formally convicted or even charged and retains the right to a fair trial (should he ever wish to take it) but removal of eligibility would be a civil matter.
I think this would be a dangerous precedent. A fundamental principle we have is inclusivity and for inclusivity to have meaning it has to extend to those for whom we have no time at all. Chess players must be judged by their chess playing. Clearly had Brian Eley behaved in a way that disrupted the functioning of chess that is a ground for exclusion, but the incomparably worse things of which he is accused, even if he were to be convicted, is not grounds. To veer from that opens the door banning people from the game for anything generally considered unacceptable behaviour but unconnected with chess. In the past century that could have been jewishness, pacifism, communism, gayness.. By and large chess has always resisted such exclusions, but not all sports have. Would we, for example, still want to bar Eley if he were convicted, served his sentence, and then wanted to resume playing chess? We might find it a challenge how to behave if meeting him over the board, but I firmly believe he should be allowed to compete in such circumstances.
[Declaration of Interest: Brian Eley coached me as a teenager. I don't think that's affecting my judgement here. I never liked him as a person: he revealed some rather nasty aspects of his character (card sharping) though I never saw any sign of sexual impropriety. However, the allegations did not surprise me (though at the risk of sounding facetious, it did make me wonder why I wasn't pretty enough)].