"A council property is not the same as a private tenancy. You do not need permission for every small amendment you want to make. The councils usually WANT you to make these changes as it saves them the time and money. (speaking from my experiences with my own Local Authority, cant say this is an across the board thing)*
It certainly isn't an across the board thing. The council here are strict and made one of my clients pay for an inspection because he replaced the bath taps with a shower mixer himself. They insist that it is done by a qualified plumber with insurance in case it all goes horribly wrong and floods the property, and the one below if it's flats.
They've also had some bizarre things happen, like people taking out dividing walls that were load bearing and my favourite, the people who converted a small bedroom to an en suite bathroom, which subsequently leaked, and the floor collapsed while the tenant was in the bath! That happened at a house not far from me and involved the fire brigade and everything.
Levelling all or part of a sloping site isn't a simple matter unless the slope is quite gentle. I once got quotes to alter the sloping top part of my garden, and it was really complex. The quotes varied between £3k and £5k, and this was approx 25 years ago.
The possible consequences of doing a bodge job and ending up with a landslip are pretty serious.