Well, this is a little bit tricky because this is written as though you, upon renting, would take ownership of utilities. However, you can probably assume that everyone else who's signed a lease has the same agreement.

I guess the main thing is: You don't take over someone else's debt, full stop. If your landlord wants utilities to be in your name, they should draw up a new agreement that puts down, in black and white, how utilities are split among the other tenants, and I would even argue that having to take on the responsibility of managing the utilities for the other tenants should be worth a reduction in your rent. That may be pushing it, but hey.

My advice would be: speak sensibly and reasonably, agree to pay your share of what you've used so far, but draw up a new agreement, because the current one doesn't reflect the proposed usage.