Stated goal of monetary policy is low and stable inflation:
Tools for setting monetary policy are bank rate and quantitative easing or asset purchase programs.
One way to view the central bank tools is to identify the combination of the government deficit spending and private credit market system as the two drivers of aggregate demand. During war time since World War II, for example, the modern governments deficit spend, cause full employment, and shift resources from domestic consumption and investment toward war time uses, and this would cause inflation unless the government and/or central bank institute policies to curb high inflation. Take away government deficit for war spending and you are left with the peace time deficit and private credit system as drivers of high inflation. The central bank increases the bank rate to reduce inflation caused by the combination of government deficits and private credit market activity. But if there is deflation then bank rate cannot be decreased below zero to stimulate the provision of credit so this is called the Zero Lower Bound (ZLB). Quantitative easing is used at the ZLB but does not necessarily stimulate credit formation to generate mild inflation.
During a modern financial market crisis the banks and other financial intermediaries have problems with solvency and liquidity. Banks and financial intermediaries (FI) develop a liquidity problem (modern bank runs) when the depositors or investors in the FI suspect that a solvency problem will begin to wipe out equity claims due to bad loans in the asset portfolio. The so-called global financial crisis was triggered by solvency concerns and developed into a market crisis where banks and FIs could not develop liabilities or place new paid-in equity to keep cash flowing in the payment system. The central bank had to provide liquidity to keep the solvency problems from getting worse due to market reaction to the solvency problems.
Quantitative easing (QE), also known as large scale asset purchases (LSAP) or asset purchase programs (APP), injects liquidity into the aggregate bank sector when the central bank purchases financial assets from banks and/or nonbanks. So if the goal is to solve the liquidity problem during a financial crisis then QE may be a solution to this part of the problem. But if the goal is to stimulate bank lending or lending by financial intermediaries to stimulate the economy then QE may not be a solution.
I don't know about the finance in United Kingdom. In the United States during the 2008 financial crisis the FDIC increased the amount of insured deposits; the Fed injected reserves and deposits into the aggregate bank sector by buying securities from non-banks; the Fed paid interest on excess reserves (IOER) to keep banks from purchasing short term Treasury securities paying lower rates of interest than the IOER policy rate; the banks and Fed purchased mortgage-backed securities guaranteed by the Treasury through the federal home loan guarantee programs; and the nonbanks purchased more short and long term Treasuries to hold in their liquidity cushions. This means the combined actions of Fed and Treasury provided more central bank liabilities and federal government liabilities to hold in the aggregate bank and nonbank liquidity cushions and probably this was not a policy accident but a plan by the leaders of the central bank and Treasury to help the markets adjust to the crisis with less deflation than without a bailout.
So the combined actions of FDIC, Fed, and Treasury provided liquidity to both the bank sector and the nonbank sector. In general the Fed and banks purchased assets guaranteed by Treasury paying higher interest (Agency and guaranteed MBS) and the nonbanks held the Treasury securities paying lower interest in the period after the federal government expanded the Treasuries float and federal guarantee in the asset pools called mortgage-backed securities. One purpose of these programs was to provide liquidity. Another purpose might be to allow bad debts to be written down by the banks and financial intermediaries while the government helped the banks to recapitalize. Another concern would be to use deficit spending and/or monetary policy to stimulate the economy so it would not go into a deep recession and QE may not be effective at solving that macroeconomic problem. But I think QE would provide liquidity and help banks recapitalize compared to a counter-factual outcome where the government lets the markets determine winners and losers by portfolio allocation decisions made during a financial panic.