Yes and no. Yes, QE kept interest rates low so government can borrow in a very affordable way. We pretty much borrowed from ourselves to pay for furlough etc. We’ll never create enough tax to pay our way so borrowing is essential. Our tax take is what, 33%, we take much less than other G7 or EU countries, but even if tax levels get higher (as they should through corporation and tax on higher earners) we will still need to borrow. That borrowing doesn’t create inflation. We still borrow much less than France, Italy, Japan and the US. I’d argue we could borrow more at these low interest rates, but there’s the moral twitchiness of mainly Tory voters who hate the idea of borrowing and are hooked on Osborne’s living within our means mantra - which will never happen. And look where 10 years of austerity got us.
QE has obviously increased the supply of money, it helped the balance sheets of banks, and the liquidity has reassured, but it hasn’t caused inflation. But the investment has gone into assets, not GDP, if you’re big enough to access the capital markets, great, if not it won’t help your growth. Banks didn’t really use it to lend to increase GDP.
There’s now a strong argument that QE could be used for a national development bank, as they have in Germany, Brazil etc. Strategic QE - public money for public benefit, so yes, a money tree, but not one that creates inflation by simply chucking money at people, a tree which develops the real economy, not just the markets.