I'm sorry, I just don't subscribe to this.
As regards a family on a low/no income, the vast majority of their purchases don't attract VAT, e.g. food, children's clothes, newspapers say etc With the level of VATable purchases they make the couple of pence in the pound really isn't going to make a difference.
B2B transactions have no net VAT effect.
In the middle you have people who have some disposable income, are you trying to tell me that someone spending £500 on a TV will be more inclined to buy it for £490 than £500, no they'll buy it anyway. The government loses out on a tenner & the customer pockets the £10 & may or may not buy themselves a pint in the pub on Friday night, or they were going to the pub anyway, so they probably won't.
Surely, you'd be better off spending the £12B on an infrastructure project, road building or repair for example, which provides actual employment to people who will then spend that money on buying stuff.