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) <You'd accept> and <Letter is full> and b) <You'd refuse> and <Letter is empty> from being true, because your choice cannot determine the outcome of the cointoss Alpha made. Thus, you should accept.

<I predicted that you will refuse this £10> 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.