If there's a water company worth £4 billion making £500 million a year profit, the government "prints" £4 billion and buys the company, then every year "burns" half the profit and reinvests the other half. Would this work or create damaging inflation in the economy?
This is a transaction where productive assets change hands, it is not a transaction that reflects production.
Moreover assume that the company oparates exactly as before, producing the same output in quantity and quality and with the same prices and with the same costs.
Then nothing has changed in the economy as regards production (and so income).
The only difference is that the previous owners of the company now have in their hand 4 billion pounds. What will they do with it?
Assume they just keep it in the bank. Then under fractional reserve banking, the bank will be able to offer more loans at a total principal value a multiple of the 4 billion. Will the bank attempt to offer more loans? If it does, will it have to offer lower interest rates to attract willing (and solvent) borrowers? The questions have no ending.
Assume instead that the owners try to spend the 4 billion by purchasing goods from domestic businesses. Is a 4 billion-increased-demand large enough to push prices up (is supply capacity at its limits and stock low) or suppliers will be happy to accommodate, no problem? The questions have no ending.
Assume instead that the owners attempt to import goods from another country...
My point is that such questions can in principle be answered only after assumptions as to the state of the economy have been clearly spelled out (i.e. only in the context of a model). Moreover, for a specific case study, the relative size of the transaction compared to the economic system matters. How is a 4-billion increase in government debt perceived by economic agents?
...and I haven't even touched and the "burning the profits" strategy proposed in the question (and it wouldn't burn it in any case, it would repay its debt to the central bank, which, granted, is the economic equivalent of destroying money).
This transaction is akin to Quantitative Easing using utility assets instead of Government bonds. Thus, the main effect is to drive up the prices of utility companies (and other private sector assets), just as QE drove up the prices of government bonds. This policy 'works' if the aim is to support the stock market, perhaps reasoning that this would create confidence in the marketplace and spur economic activity.
Since the 4bn is removed from the economy over time at the rate of 250mm per annum, I would expect the above effect to be temporary rather than permanent.