You can still gamble sensibly even when the amounts are large. For example, if the banker offered £100, you'd probably want to reject the offer. If the banker offered £124,999 then that's so close to the expected value of the gamble it's surely right for most people to just take it. If the banker offers £50,000 should you take it? How about £20,000? At some point you're getting lowballed by just too much and you have to take a stand and gamble. It's interesting (to me at least) to figure out exactly when you should accept the offer in a principled manner rather than just go by feel.
A good model is to for you to take the choice that maximizes the expectation of the log of your net worth. So if you have £X in the bank you want to accept an offer of £Y if log(X + Y) > 0.5(log(X + 0.01) + log(X + 250000)). Using logs captures the idea that, for example, if you have no money than £1M is worth a lot to you, but if you've already got a net worth of £10B, then another million isn't worth that much.
Using that model, and in the case where Y=£88,000, you need to already have approximately £110,000 to rationally reject the offer and take the gamble. That's a significant amount of money, but it's not unreasonable to believe that this woman had that much and so made a rational and good choice.