The 0.5 per cent rise compares with a rise of 0.1 per cent between the same period a year ago.
The largest contributor to the rise was university tuition fees as this is the first year students have to pay the new fees of up to £9,000. Prices for education rose by 19.1 per cent between September and October, more than twice the size of next biggest monthly increase since CPI records began in 1996.

Food and non-alcoholic beverages were the second largest contributor, particularly potatoes and confectionary. The fact many confectioners had reduced the size of their products was treated as a rise in CPI and RPI as consumers get less for their money.
The most significant downward contributions came from housing and household services which rose by 0.1 per cent compared to 0.6 per cent a year ago and recreation and culture which rose by 0.4 per cent compared to 0.7 per cent a year ago.
Retail prices indices inflation, which includes mortgage payments, stands at 3.2 per cent, up from 2.6 per cent.
In last month's minutes from the Monetary Policy Committee meeting, the committee said inflation was not falling as fast as it had hoped and expected inflation to remain above its target two per cent for the rest of the year.