This is more of an issue to take up with the local council, you wont be breaking any laws, more of a planning issue. The council will evict if you try to live in the tent on their property.
If she lives alone, and claims Council tax rebate, she will now have to pay the full amount. Unless you are paying council tax yourself for some other address. If you stay there for weeks or months, she will have to add you to the electoral roll.
Hard to say really. My friends have had a large Yurt up in their garden for the last 8 years and use it as part of the house- no-one's ever said anything or come round about it to my knowledge, but that's a private house not a council house.
But why would you want to live in a tent in a garden in winter? Is there no room in the house or have you been thrown out?
No harm in putting up a tent and staying a few nights but if it becomes permanent then I think you'd need to contact the council to get permission. The same thing apples when people try and live in caravans in their gardens or driveways - temporary is ok but permanent is a no-no.
The yurt issue is like having a marquee - it's not for residential use. Living in a tent will increase the number of residents in the dwelling, if it's long term. Your sister may not be allowed to sublet a room under the terms of her tenancy agreement - I would think that living in the garden (if you do it for more than a few days) would fall into the same category.