For example, people may choose to save their money, or not borrow (given higher interest rates), instead of buying fuel, but that is unlikely to affect it's price.
This seems more like an attempt to strangle wage increases.
For example, in the US, recent interest rate hikes led to even larger mortgage rate hikes. The increase in mortgage rates had the effect of making it more difficult for people to afford homes. Once mortgage rates started rising here, I started to see a reduction in homes sold and it has started to lead to a slight reduction in home value.
It is that and more. There aren't many levers to pull but one that is available is interest rates which in a kludgy way allows you to slow down investment in businesses which in turn results in preventing wage increases, hiring, and eventually results in an increase in terminations or eliminating positions. Less money going to workers means less money can be spent in the economy and less demand for goods and services. Inflation then drops or depending on severity bursts some bubbles and enters into a deflationary period. So yes the whole point is to cause painful decreases or elimination of wages.
The issue right now is that demand is actually being ENCOURAGED by low interest rates and continued quantitative easing. Don't be fooled, 2% is still a low interest rate historically speaking.
Basically spenders need to be encouraged to save.
Low rates -> more money flowing into housing markets -> higher rents