It is an empirical question, and so I have tried to find data to provide an answer. I was not happy with my first go because the data I had was for nominal interest rates. To strip out any effects of inflation I have found data on real interest rates from the world bank. Combining this with the ONS data on savings rates (via the BoE) for 1967-2009, I have produced this scatter chart.
|Source: World Bank, ONS via BoE|
On a loanable funds model this implies a vertical supply curve, just like my old textbook said.
The same caveats as yesterday apply. This is one country over one period and done in a rush. Other empirical analyses are welcome.