Agreed. I was merely disagreeing with your statement that "the £350 is not taxable". It is taxable.
And also, with respect, your comments about ISA's above are a bit irrelevant. You were suggesting how someone can make £350 by switching bank accounts.
Incidentally, I am not entirely sure that the £125 isn't taxable either. In the case of cash backs on purchases, it is not treated as income, but as additional disount on the purchase price and is therefore not subject to income tax. In the case of switching accounts, where you are not "buying" anything, this is moot. It would be interesting to hear how the HMRC views this.
But overall, I do agree with you that most people reading this thread would not have to pay tax on the £350.