Spend lots and lots of money and the resultant higher economic activity may actually boost the coffers to compensate (or part compensate) for the spending. There are some respected economists who buy into that theory.
The problem is that there are also lots of economists who think that's complete bonkers i.e. there's a high chance the plan will backfire.
It's called
'The Paradox of Thrift' and is one of the more well known paradoxes of economics.
Economics is full of amazing and fascinating paradoxes. Wikipedia lists over 30 and there are many it does not list, such as the 'Bus Paradox' (one bus per day remains empty, but 10 busses per day are used intensively) or the 'Lump of Labour Paradox' (a reduction in hours worked by all leads to an increase in unemployment) but Wiki does list my favourite, the 'Tullock Paradox' (bribing a politician costs less than one would expect, considering how much profit it can yield).
The Paradox of Thrift is one of the many such paradoxes, which come from the general principle that,
what may be beneficial for an individual, is no longer beneficial for a much larger body or more complex economic entity, such as a business or a country.
It is better for the individual to save, as the long-term returns for saving are far, far greater than the long-term returns for spending. However, that simple observation cannot even be scaled up to your local corner shop. The proprietor cannot save his shop from failure by cutting back on buying in stock or getting rid of his delivery van.
According to Picketty in his massive work 'Capital in the 21st Century' nations grow on average at a rate of about 1% p.a. in real terms, whereas capital grows at c.a. 4%. In order to achieve the higher growth rate of capital, a nation has to invest in that capital. Just spending money ad liberatum would indeed be bonkers, but if you look at the very rich nations of Europe, they have all invested heavily in infrastructure - something the UK has very noticeably failed to do.
As you once brilliantly pointed out, there is no need for speed cameras on the M25, as the traffic is more or less at a permanent standstill and portrait painters would be more appropriate. The motorways are too narrow, the trains are slow, expensive and unreliable, broadband coverage is patchy, the health service compares very poorly with the rest of Europe, educational standards are falling - and so on!
Britain tried austerity once before, after the Napoleonic Wars and the result was the largest fall in living standards the country has ever seen in peace time. It didn't work then and it cannot work now.
That should not mean that we waste money - the MoD does not need 55,000 civil servants, in fact, it probably doesn't need 5,000. We should not be subsidising the wilfully economic inactive. We should not be throwing money at the underpaid, thereby subsidising inefficient companies. And we certainly should not be giving N.I. £1bn to cure the problems that they created all by themselves and for themselves.