I'd refuse the £10 unless I was extremely confident (>99.999%) that if I took the £10 I couldn't actually exist because the scenario as given was inconsistent and that the real me would end up with £10 more if this was true.

(i. e. the offer was independent of my decision but the prediction not, Omega would take exactly the same action regardless of whether the envelope was filled, the prediction would be false if I took the £10 in either case, and I would take the £10 in either case)