Listen Sweetheart, you BROKE THE LOCK, so YOU PAY FOR IT!
You are not in a hotel! Also try reading the Terms & Conditions of your Assured Shorthold Tenancy Agreement - presuming you can read at all that it.
If you borrowed your friends car and broke the key in the ignition, would you expect them to pay for it? NO!
Finally, try getting a job and you wouldn't need to be harping on about how hard-up you are and expecting the tax payer to pay for your rent, the local council to pay for your council tax, benefits to pay for you and your children, and the landlord to pay for damage to his property that YOU caused through your own incompetence.
Also interesting that you have money to go ice skating but no money to pay for the damage you caused. Hmmmm?
Take responsibility for your own actions.