I should perhaps concede that I'm not an economist, so I can't personally judge the soundness of Friedman's argument. What I would say, though, is that wage increases are evidently not the sole, nor even the primary, driver of inflation, as shown by the graphs in the LSE link. It also can't be the case because of common sense. Taking bobbinwales's arguments literally, it might be argued that any wage increase at all would be somehow dangerous as an inflationary pressure. At the very least, any wage increase should be at most limited to ( or even be slightly below?) the rate of inflation at all times, for to push it above that rate would surely, by this argument, always drive the inflation rate ever higher.
It's not a sustainable argument. Even if Friedman has oversimplified his explanation of inflation as merely a reflection of the total quantity of money -- apparently an ongoing debate in economic theory that is way over my head -- it should be uncontroversial that wage increases aren't something to be feared or suppressed, but welcomed, as a reflection of economic growth and aspiration.
Salaries in the public sector have anyway been relatively stagnant for over a decade now, since around the financial crisis and, in this country at least, since the 2010 election and the resulting change in fiscal policy. I don't here intend to blame the Tory Government for this -- in particular, you can point the finger for the present spike in inflation largely at the twin pressures of Covid and the Ukrainian War -- but since both of those are recent, they can by definition not account for the previous ten years of virtually flat, at best, public sector pay. Depending somewhat on the source, real-terms teacher pay has decreased by around (or sometimes more than) 10% as it is in the last 13 years or so, which is even reported in OP's link (see also
https://ifs.org.uk/articles/what-has-happened-teacher-pay-england )