The "natural rate of interest" is zero. Unless the Bank of England offers interest on reserves or the Treasury issues Gilts banks will try to lend out excess reserves in the interbank market but won't be able to in aggregate. The rate will fall to zero.
As Neil Wilson says:
"If you and I have only £10 between us then there is a limit to how fast we can move it between us in exchange for goods and services. That's the natural friction within the system (and is lower in the financial sector which is how it appears it generates so much money. Really its just a velocity shift).
However if there is more money in the economy - say £1000 then we can each have savings and still have enough liquidity to move real goods and services between us as fast as a possible in the real sphere.
Which is actually what we need.
The belief that is wrong is that the system naturally has enough liquidity. It doesn't. The unemployed have insufficient liquidity to demand the goods and services they need, which if they could would actually result in them being employed.
And the paradox of thrift caused by financial saving just isn't automatically offset by sufficient loans from banks. The market doesn't 'clear' at full activity, the quantity wanders up and down dependent entirely upon its own dynamic and with little direct connection with the real activities that need financing.
Money is made round to go around. What matters in turnover of money stock, not the size of the money stock."