you may be over-reacting.
Blocking Cheats

was the game in live chess or online chess?
I am not talking of any particular game. I really just wanted to know.

Yup, you can block anyone for any reason you wish.
In the case of cheats, I'd suggest you report them too. Thin out the population for the honest players.

@OP: All discussions pertaining to cheating are best conducted in the Cheating Forum.

This is all a bit weird, Look, all I do is read posts while waiting my turn during a game. I read a couple on cheating and it got me to thinking, what would one do if they felt someone was cheating.
I thought, would it be possible to block a member if you felt they were cheating, that is all.
I think a quick look at my games would make it painfully clear, that I am not qualified to determine if anyone was cheating.
This is why I stated it was for future reference.

Yup, gotcha. I'm just saying if you ever come across one you should report them.
As for blocking them, yes, you can block anyone you like, for anything you like.
I think Whirlwind's point is just regarding cheating in general. There are rules about naming and shaming on the forums etc. This thread doesn't come under that category so no big deal.

@Sunofthemorninglight: How so? My post contained no hint of chastisement. We have a group for discussions of cheating, and this topic would fit right in. If the OP would like to inquire further into topics related to cheating, he may now do so without risk of his threads being locked by staff members.
@Stevie65: Thanks for the promotion. Will you be paying my salary?
I am not accusing anyone you understand! But if I played someone who I believed to be using a computer for their moves, is there a way I can block them so I do not have to play them again?
This is just for future reference.
Simon.