UK inflation held steady in June despite hotel prices rising strongly, according to the latest official figures.

While prices in restaurants and hotels went up, sharp falls in clothing helped offset this as retailers offered widespread sales to shoppers.

Overall, inflation rose at 2% in the year to June, unchanged from May.

It means that the cost of living is still rising but at a rate that the central bank is comfortable with, after nearly three years of above-target inflation which has squeezed household finances.

The latest data showed that prices in restaurants and hotels rose more than a year ago, putting upward pressure on the headline inflation rate.

Hotel prices soared by 8.8% compared with the previous month, the Office for National Statistics (ONS) said, whereas prices in restaurants and cafes went up by 0.3% on a monthly basis.

It also showed that the costs of package holidays, cinemas, theatres and concerts were rising.

But prices of clothing and footwear fell last month, while food and drink inflation has dropped sharply from the highs of recent years.

The figures on Wednesday also showed that second-hand car costs fell but by less than the same time last year.

However, in areas like services, which include everything from restaurants to hairdressers, price increases remain persistent.

That could raise questions for Bank of England policymakers over when they should begin to cut interest rates.

Darren Jones, the new chief secretary to the Treasury, said that families’ budgets across Britain were still being squeezed.

“We face the legacy of 14 years of chaos and economic irresponsibility. That is why this government is taking the tough decisions now to fix the foundations so we can rebuild Britain and make every part of Britain better off.”

The Bank’s base rate – which is used to help set mortgage rates and other borrowing costs – currently stands at a 16-year-high of 5.25% after it was increased in a bid to tackle soaring inflation.

Its Monetary Policy Committee (MPC), which votes to set the rate, has held interest rates at this level for several months but some economists have predicted they will cut the rate at the next vote on 1 August.

Leanne Morgan and her husband Gareth bought their house in Greenwich, south-east London, in 2016 when interest rates were much lower.

Their five-year fixed mortgage deal came to an end this month and their new rate stands at just over 4% – pushing their mortgage payments up by £5,200 a year.

Mrs Morgan said the higher mortgage payments had restricted the things they were able to do with their three older children.

“We can’t have family holidays, we’ve not been able to do so much with the children….it affects where I shop for food, I’m always looking for discounts. We sit together, we look at what our costs are, where we can cut back and look at a budget.”

She said was optimistic, however, that the UK economy was over the worst and that better times were ahead.

“I think sometimes the doom and gloom that we talk about can actually make us feel very negative….It you can feel hopeless,” she said.

“But if we have a good conversation about what is possible, and working with what we’ve got, we can have a better conversation about it,” she added.

The underlying measures of inflation being watched closely by the Bank of England also did not change, according to the latest data.

Inflation in the services sector, for example, remained at 5.7%, while core inflation, which strips out the effects of more volatile items like energy prices, held at 3.5%.

Alongside some other stronger figures for the economy in recent days, it may give some pause for thought for members of the Bank of England committee deciding interest rates next month.

On Tuesday, the International Monetary Fund listed the UK among countries who might need to keep interest rates “higher for even longer” than originally anticipated to squeeze inflation out of the system.

Markets have been anticipating that rate cuts will start on 1 August, helping fixed mortgage rates fall.

The latest numbers suggest it will be a finely balanced decision.