Same as it's doing now actually but instead of giving it directly to the banks you put it in the hands of Joe Public who will spend it(unlike the banks who are using it to try and wipe out toxic debts imported from the US) and get the economy moving again.
The idea of borrowing to fund investment is quite popular at the moment. This isn't the same thing as a Keynesian fiscal stimulus, which was about increasing consumption rather than investment.
I have concerns about the viability of either though. The point would be to increase aggregate demand and/or employment in the short to medium term. I can't quite get beyond the following:
1. Where will the money come from? The UK may be able to borrow at low rates, but bond markets continue to monitor and punish countries for a lack of fiscal control. People have argued that bond markets shouldn't dictate government policy. If that is the objective then governments shouldn't borrow so much money. The alternative is to print money, and there are two versions: make it clear that the increased money supply will be reversed (which has implications for what people will then do with the money) or don't unwind it in which case, as Napster points out, this is inflationary.
2. What to do with the cash? Assume we can get it, do we send everyone a cheque (as you imply Barna), buy corporate debt to increase liquidity in the corporate sector or fund public investment projects? Sending a cheque to everyone would target consumption spending rather than investment. However, there are two problems. The world has moved in since the 1930s. Globalisation means that some consumption spending would leak outside the UK (the UK giving money to citizens to buy Chinese goods), but the greater problem is that the UK was the most leveraged country in the world in 2008 (government, corporate and household debt). If everyone received £1000, how many would use it to pay back debt? If they did there would be no increase in consumption. All that actually happens is household debt is transferred to the government.
The problem with investment is that it takes a long time to deliver. Again, this is not the 1930s. Planning law has moved on considerably. It takes 3 years to acquire land and planning permission before a construction company can lay the first brick of a housing estate. Large projects, such as HS2 or a new airport, would take 15-20 years. I'm not saying that these aren't worthwhile projects (I think they are) but they won't do any good to short-term growth.
Finally, the employment issue. In the 1930s shovel ready projects were easily staffed by local blue collar labour. The benefits of increased employment flowed through the economy accordingly. However, there was no migration then nor a welfare state. As I have pointed out before, we have a test case in the UK for infastructure investment: the Olympic Park. The borough of Newham hasn't seen a reduction in unemployment or welfare spending as the project has sucked in immigrant labour. The same would happen across the UK.
The UK economy has two problems: the banking system is bust and, for various reasons, long-term trend growth has reduced (a number of economists think the economy's capacity to grow is now about 1% rather than 2.5%). A fiscal stimulus won't fix these problems in the medium term and investment spending is fiddling at the margins in the long-term.