You are correct, per according to Consumer Price Indices: a brief guide by the Office for National Statistics (directly indexed pdf, so google the name to find), here are some selected examples of UK CPI factors and their weights.
Class: Weight
Food: 93
Alcoholic beverages: 20
Clothing: 59
Actual rentals for housing: 62
Electricity, gas and other fuels: 48
Purchase of vehicles: 38
Other recreational items, gardens and pets: 32
Education: 21
Restaurants and cafes: 88
These weights feel intuitively off to me, but I imagine costs like rent and education look low because only a subset of the population is paying for them, even if they are huge cost to members that cohort.
Aren't rents included in the CPI? I would be surprised if they weren't since it's a pretty huge part of most people's monthly expenses.
Then it would either mean that the rents rose along with the house prices (in which case this effect is included in the inflation figures) or that the actual housing costs didn't increase -- it's just less profitable to buy and more to rent.