And the same thing was true during the bailout. 99% of that money was never spent so it didn't have any affect on the economy.
Then where did it go?
The BoE then collected and destroyed government payments on the bonds, so the net amount of money doesn't change in the long-term.
One side-effect of this is that the cost of bonds went up -- demand had increased -- so the profitability of buying them went down, meaning the banks were naturally incentivised to do something else with that money.
It's not a panacea, but it is quite a neat lever to have when you want to increase the supply of money without actually spending any. Unfortunately it still looks like the banks are being given lots of free cash, but it's not actually free.
Basically the Fed made lines of credit (with strings attached) open to banks to guarantee liquidity, increasing trust in markets. Banks didn't withdraw the money, and some that did (or were forced to take it to dissuade bank runs on the others) paid it back quickly to get out from under the strings.
Here's [1] a decent source on the finances of the bailout (which were actually loans).