You're missing the fact that Alpha sending a letter happened regardless of Omega, and thus regardless of what you choose, you'd get £1 000 000 from Alpha 50% of time. You can't choose so that you'd get £1 000 000 zero percent of the time simply because your choice doesn't affect that.

I repeat that, since that seems to be the key problem here. Alpha flipped a coin to decide whether or not to send you £1 000 000. Your past or future actions don't have any control over Alpha doing this, and sending you £1 000 000. In particular, your actions, upon receiving the envelope don't have any, direct or indirect, entanglement with what does the envelope contain.

Your actions however are entangled with whether or not Omega comes along to offer you £10. If you're the kinda guy to accept the £10, Omega makes this deal only when Alpha didn't sent you £1 000 000. If you're the kinda guy that refuses £10, Omega comes only when Alpha sent you £1 000 000.

So to maximize the expected value, you should accept the £10. That way, you get 50% time £1 000 000 and 50% £10. Otherwise you get 50% time £1 000 000 and 50% time £0