Next time, do some research first
You've mastered some basic textbook economics. But you don't seem to know anything about either QE or Murphy's proposed 'People's QE'.
Existing QE was not meant, as you propose, 'to increase M in order to prevent a collapse in P and or Q'. The Bank of England published a report very carefully explaining the transmission channels through which QE was meant to work. The idea was to push down the yield curve and thus encourage borrowing, spending, and investment. If you want to force this into your quantity equation, it would make the most to say that the point was to increase V, through higher asset prices (http://www.bankofengland.co.uk/publications/Documents/quarterlybulletin/qb110301.pdf).
Another BoE report makes it very explicit that the point of QE is NOT, as you suggest, to increase M0: 'As a by-product of QE, new central bank reserves are created. But these are not an important part of the transmission mechanism.' (http://www.bankofengland.co.uk/publications/Documents/quarterlybulletin/2014/qb14q1prereleasemoneycreation.pdf) Nor does the creation of new CB reserves necessarily amount to an *increase* in M0, since, as the same bulletin explains, the BoE *always* supplies banks with the reserves they require given their volume of lending, QE or no QE. The reserves supplied via QE thus let the BoE off the hook with regard to supplying reserves through other channels; the net effect on M0 is then zero.
Murphy's PQE is no less reversible than existing QE. In the existing version, government bonds are bought by the BoE. In Murphy's version, the national investment bank (an agent of the government) issues bonds, which are bought by the BoE. In either case the BoE can stop buying the bonds, if, for instance, it starts to worry about missing its inflation target. Then, as you say, the issuers of the bonds will need to sell them on the market or retire them using tax revenue.
The idea is that if PQE adds enough investment to get the economy growing at a healthy rate, the resulting increase in tax revenue can finance the retirement of the bonds. Then the BoE doesn't need to keep buying them. It's the same if private investment picks up; this eliminates the need for PQE and also supplies the tax revenue required to end it.
You need to understand how the policies work to have a productive debate on this. That requires doing some empirical research into the institutional frameworks; you can't find the answers in the back of an A-Level textbook.