What happened to the money multiplier after QE? QE meant that the monetary base increased dramatically, yet we don't see such a large reaction in money supply (I am thinking of M4 for the UK) nor in inflation. Why is this money not being lent out? Are banks keeping large excess reserves for fear of a crash?

I know this is a quite common question but I still don't understand what the accepted answer is here.
You may want to look at the following paper by Cukierman (2017). The author compares inflation for a period of identical base expansion in post Lehman US and hyper-inflationary Germany in the 1920s. They mention exactly what you said, that banks have increased their reserves at the Fed. In the US this has not translated into a heightened demand for goods and services as was the case in Germany. Furthermore the author cites fundamental differences in the economical and institutional circumstances as a reason for the difference in transmission. I suggest reading the paper for a more in depth explanation.