On final day of China trip, PM says taxes can be lowered as deficit is reduced and promises 'significant tax cut' in April

David Cameron has said that it is possible to cut taxes and reduce the fiscal deficit at the same time as the economy recovers.

Amid fury in Downing Street at reports that the prime minister has ruled out tax cuts for middle-income earners for the next decade, Cameron said that reducing the deficit and cutting taxes were not alternatives.

Speaking in the Sichuan capital of Chengdu on the final day of his visit to China, the prime minister told the BBC: "The two aren't alternatives. It is possible to reduce people's taxes as your economy recovers. In April, there's going to be another significant tax cut as we complete the programme of allowing people to earn £10,000 before they pay any income tax at all. That's worth over £700 to the typical taxpayer."

The prime minister spoke out after the Daily Telegraph reported that the prime minister had ruled out tax cuts for middle-income earners for the next decade to allow the government to help low income earners by raising the personal tax threshold. The Telegraph seized on remarks by the prime minister, who said in Shanghai on Tuesday: "I'm a fiscal conservative; I believe the first duty of government is to safeguard our economy, and the economy isn't safeguarded properly until you deal with your deficit and make sure that you're in a position where future problems that could come down the road, you're able to absorb them."

A No 10 spokesman said of the Telegraph report: "This is a strange and inaccurate interpretation of the PM's comments."

The prime minister qualified his remarks on tax by reinforcing George Osborne's commitment to try and run a budget surplus in the next parliament. Tories on the right fear this will make tax cuts more difficult.

Cameron told the BBC: "We are going to be looking ahead to a time when, yes, if the economy continues to grow and, as it were, the sun continues to shine, we should be fixing the roof when the sun is shining, as the last government failed to do.

"That means not just getting rid of out debts in good years but trying to put some money aside. That is what Britain should be trying to do."

The prime minister was speaking in Chengdu shortly before flying home to be back in Britain in time for Osborne's autumn statement on Thursday.

The prime minister said of the chancellor's statement: "We have been working to a long-term plan, and what you are going to see in this autumn statement is the next steps in that long-term plan, a long-term plan to turn the country around, to get us out of our difficulties with debt and deficit and to secure jobs and recovery for all our people – a recovery for all. That is what we want to see.

He said the plan "involved difficult decisions about spending, about getting our deficit down" but claimed: "We are on the right track, we should stick to that track, recovering our economy getting jobs for our people and over time really fixing for the long term the mess we were left in the public finances."

The prime minister confirmed that he has no further plans to meet the Dalai Lama after the Chinese reacted furiously when he met Tibet's spiritual leader last year.

Asked by Sky News whether he could afford another meeting the Dalai Lama, Cameron said: "I want a good relationship with China. That's in Britain's interests. It's in Britain's interests economically because of the jobs, because of the investment, because of the growth that comes to our own country from trading with this country so clearly on the rise."