The annual rate of inflation was always going to fall in October and the only real question was by how much. In the end, the decline from 6.7% to 4.6% was chunkier than expected and the biggest in more than three decades. That brought some welcome good news to the prime minister after a tricky few days. The main reason for the sharp drop in inflation as measured by the consumer prices index was that the increase in energy prices in October 2022 was not repeated. Gas prices fell by 7% last month, having risen by almost 37% in the same month a year earlier. However, the slowing of the annual rate was not only because of cheaper energy. Food prices rose by 0.1% this October compared with a 2% increase in October 2022. Hotel and restaurant prices were flat, having risen by 1% a year earlier. All of which meant prices overall showed no increase between September and October 2023, compared with a 2% month-on-month jump a year earlier. The consequent fall in the annual rate allowed Rishi Sunak to announce on Wednesday he had met one of the five pledges he made at the start of the year: to halve the inflation rate during the course of 2023 from its starting rate of 10.7%. Even so, the UK’s inflation rate remains higher than in the US (3.2%) or the eurozone (2.9%). Strictly speaking, controlling inflation is the job of the Bank of England, not ministers, and whether the government gets any credit from the public remains to be seen. The easing in the annual inflation rate does not mean prices are coming down, simply that they are rising more slowly than they were. Food prices, for example, are 30% higher than two years ago, while gas prices have risen by 60%. It is a bit early to say the cost of living crisis is over, although the end is coming into sight. What is more, the fall in core inflation, which excludes volatile items such as energy and food, was much less spectacular than the drop in the headline rate. When it comes to deciding on the future course of interest rates it is core inflation that matters to the Bank of England. The two main measures of core inflation looked at by Threadneedle Street are the all-items consumer prices index with energy, food, alcohol and tobacco stripped out, and inflation in the services sector. The first of these fell from 6.1% to 5.7%, the second from 6.9% to 6.6%. While services inflation came in lower than the Bank was anticipating in its quarterly monetary policy report earlier this month, it is still too high for its nine-strong monetary policy committee to be contemplating cutting interest any time soon. That said, the latest inflation figures have left the financial markets convinced that official borrowing costs have peaked at 5.25% and they are now anticipating the first cut in rates by the middle of next year. Mortgage rates had already started to come down before the better news on the cost of living. According to Rightmove, the average five-year fixed home loan rate is now 5.30%, down from 5.75% a year ago. Further cuts in the cost of mortgages can be expected.