Let's see...
I predicted that <you will refuse this £10 if and only if there is £1000 000 in Alpha's envelope>.
This seems natural way to do it. However, if you're the type that refuses, Omega can't be making this deal when you didn't receive £M. Also, if you accept, Omega can't be making this deal if you really won. However, there really isn't anything that prevents that a) and and b) and from being true, because your choice cannot determine the outcome of the cointoss Alpha made. Thus, you should accept.
if and only if there is £1000 000 in Alpha's envelope.
This would be weird. For Omega to make a claim like this, your choice has to be somehow connected to the outcome of the coinflip Alpha made before sending you the envelope. This is because Omega is making the prediction conditional only to the outcome of the coin toss. Your choice is simply assumed to be entangled with that.
This is a variant built on Gary Drescher's xor problem for timeless decision theory.
You get an envelope from your good friend Alpha, and are about to open it, when Omega appears in a puff of logic.
Being completely trustworthy as usual (don't you just hate that?), he explains that Alpha flipped a coin (or looked at the parity of a sufficiently high digit of pi), to decide whether to put £1000 000 in your envelope, or put nothing.
He, Omega, knows what Alpha decided, has also predicted your own actions, and you know these facts. He hands you a £10 note and says:
"(I predicted that you will refuse this £10) if and only if (there is £1000 000 in Alpha's envelope)."
What to do?
EDIT: to clarify, Alpha will send you the envelope anyway, and Omega may choose to appear or not appear as he and his logic deem fit. Nor is Omega stating a mathematical theorem: that one can deduce from the first premise the truth of the second. He is using XNOR, but using 'if and only if' seems a more understandable formulation. You get to keep the envelope whatever happens, in case that wasn't clear.