Wednesday's meeting of the Monetary Policy Committee will be shown the letters and then King will be allowed to take the Bank into the unknown. Normally the nine members of the MPC discuss interest rates, but having cut them to just 1 per cent this month, they have almost reached the end of that road. Now, instead of debating the price of money, the MPC will concentrate on the amount of it.
Quantitative easing allows the Bank to buy gilt-edged securities or corporate bonds from City institutions or through the market. As the Bank will not itself borrow the £100bn or more necessary, it is in effect printing money.
The theory is that providing liquidity to the banks or insurance companies that sell the debt, will mean they have new funds to lend to businesses, homebuyers or consumers who are currently unable to borrow.
Yet the theory has never been tested in Britain and no one knows whether it will work, never mind how well. Vicky Redwood, consumer and debt specialist at research consultancy Capital Economics, says: "It depends on how vigorously the Bank embraces it. The main danger is doing too little."
Japan's central bank adopted quantitative easing in 1990 when it had cut interest rates to zero. It bought bonds for five years, but the jury is still out on how effective the policy was. Tokyo is considering repeating the exercise now, however, and the US is likely to follow Britain.
But just as interest rate changes take months to influence the economy, quantitative easing is not expected to have any immediate effect. Whether that result comes sooner or later, or is bigger or smaller, than the interest rate changes is unknown.
The MPC might decide it is not working and increase the buying programme, only to find the delayed effect of the early buying is more powerful than expected. But if the effect is slower or weaker than assumed, the committee could waste several months before it realises it needs to buy more stock.
"At least we have a past relationship to look at with interest rates," says Redwood. "With quantitative easing we can look at the Japanese experience, but the main practical difficulty is knowing what to do and how much."
Money supply has been out of fashion since the Thatcher government, as inflation has become the economists' lodestar. But now with the prospect of quantitative easing, which boosts M4, the broad money supply comes back into the limelight.
Normally the Bank uses its reserves to keep the base rate at the set level by buying or selling government securities. However, by increasing the supply of central bank money, it can directly raise private-sector spending by giving funds to sellers of bonds, or indirectly do it by expanding the lending banks' supply of credit.
The MPC has turned to this new tool because it fears any more interest rate reductions could be counter-productive. At this month's two-day meeting, it was told that rate cuts alone would probably not return inflation to the government-set target and that the stimulus from cheaper borrowing reduces when rates are very low.
"The short-term market interest rates that the base rate sought to influence could not go far, if at all, below zero," the committee agreed. "Indeed, there might even be a point at which further cuts could have an adverse impact on the economy."
Many savings rates are already almost zero and cannot be negative. Banks would either have to squeeze their profit margins to cut lending rates further or would not pass on new reductions. But with lenders having to reduce rates on tracker mortgages, banks that do pass on cuts would reduce their profits and thus erode the capital that allows them to lend.
At its last meeting, the MPC thus unanimously agreed that King should write to Darling. But while drafts of his letter and the response have been prepared, the terms and extent of the programme are not yet agreed.
King wants to be allowed to buy bonds from blue-chip companies as well as government stock, to get funds to the business sector more directly. Japan went further in the 1990s by buying shares, and last week said it was considering doing so again. A central bank could also buy illiquid assets such as property or lend to companies directly – but Darling and King are planning nothing so radical.
With a high budget deficit, Darling has plenty of gilts for the Bank to buy. And if the buying pushes up bond prices, it reduces yields, making corporate and public borrowing cheaper. But because quantitative easing is an unfunded economic stimulus, the Government issues less stock.
There are risks, however. Corporate bonds could default. Banks might hoard cash rather than lend it. And printing money could weaken sterling while – as has happened spectacularly in Zimbabwe – inflation soars. Philip Shaw, an economist at Investec, says: "The biggest danger is that it does not work".
Darling gave the Bank a £50bn "asset purchase facility" last month to buy bonds. That is credit easing, not quantitative easing, because it is funded by the Treasury. However, the facility will be the framework for this week's even larger unfunded programme.
"Numbers like £100bn and £150bn have been bandied around," says Redwood. "That might be enough. I don't think the MPC will do that much immediately, but it might end up costing more if we don't do enough early on."
And after spending its newly printed money, the Bank must at some point resell its bonds. If it sells too soon, it risks dampening the economic recovery. Shaw thinks it could unwind the quantitative easing next year; others believe it could be four or five years before it is safe to sell the last stock.
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