If you have a consistent utility function over outcomes, you cannot be money-pumped.

If your utility is convex in money and you follow independence, I can money pump you no matter what the situation, as L will always be worth more to you than £1.50. I will continue offering you that contract until you have no cash left, an event that is certain to eventually happen. So your statement is incorrect.

If your utility function is concave in money, it's a little harder, but I can use options. Contract A will give out £1 if a coin comes up head; contract B will give you £1 if that same coin comes up tails. I offer you cash for the possibility of buying these contracts from you for free (should you ever get your hands on them), as long as your capital is within £2 of your current amount. You should name a price less than 0.50 for these options, including a small utility profit for you; I take one option out on each of A and B. I then sell you A and B together, for £1 (since together they are exactly the same as a certain £1). I then exercise both my options and get A back, then B.

Of course, you would never do anything as stupid as accepting the contracts I've just described; but the fact remains that if your utility is not linear in money, you cannot put consistent prices on contracts and their combinations, so will end up losing if ever you blindly follow your utility function.