Outraged, I don;t know your finances but entitledto is well known for being frequently wrong and doesn't take many factors into account. or rather turntous as it is now known; also worth remembering that a lot of cuts do not happen until later this or next year anyway so it doesn't reflect current situation.
I shall give an example; couple I know who have a 4 bedded council house because they were allocated an extra room due to a disability one of their children has. The new LHA rent does not take that into account so they will made to pay the spare room tax, despite it being a used, needed room. They will lose half of the tax credit disability portion as that has been cut. They will lose a significant portion of the CTB as that is being done differently- overall they are going to lose hundreds a month, and that is a family theoretically exempt from the caps.
Figures right now are NOT relevant beyond the next few weeks as universal credit trials are staring shortly in selected areas.
Forever true many could make cuts but also you are availing yourself of London infrastructure too; DH needs a car to get to his office, being rural; I need a car to get to the boys' SN Schools, which are each several miles away in opposite directions. We are trying to work out atm if I can stop driving as my eyesight won;t allow me to forever and the answer has been nope, not yet. Luckily there's a plan to build a train station here, which means I can absolutely dispose of the car keys (I hope, depending on work).
It's no different for those who live here and are elderly or out of work- transport is poor and shops so limited you won't get an apple without a 45 minute uphill hike! As our population is quite elderly, not always an option.
WRT to fuel costs- there was a proposal back along to remove it from older people living in places where the mean winter temp was warm- 20 degrees IIRC. It was shouted down by the Tory failthful. I can;t for the life of me work out how that is a justified expense. It was removed from the severely disabled some time back, yet if you are a certain age and live in a hot country with your fortune (we shall paint a stereotype here and say inherited fortune) you can get it? pathetic.
I don't know that I know many who choose not to work by the way, and I grew up on a council estate classed as deprived and worked for a charity that meant I got to know a lot of the finances of young, often poor, families. I can think of 3 individuals who meet that criteria, all acquaintances socially, but two of them have a working partner; the other has a partner who is a carer, I also happen to know via means I would not dream of specifying (not illegal- small town chat) that he is impossible to actually employ and a risk to the livelihood of any business. AS small business owners ourselves (or rather DH is) we certainly wouldn't want him anywhere near us, and we are happy for our taxes to keep him far away!