Mr Johnson also admitted the existing £9 billion support package of loans to cut energy bills and council tax rebates was not enough.
The Prime Minister is now facing an investigation over misleading Parliament after he told the Commons that no laws were broken in Downing Street around parties held while Covid restrictions were in place.
Asked whether he is honest, the Prime Minister said: “Yes. I think the best way to judge that is to look at what this Government says it’s going to do and what it does.
“I do my best to represent faithfully and accurately what I believe, and sometimes it’s controversial and sometimes it offends people, but that’s what I do.
“I have apologised for the things we got wrong during the pandemic.”
Pressed on the issue, Mr Johnson said: “With great respect, I’m going to have to ask you to wait until the end of the [Met Police] investigation.”
He added: “I will make sure that, as soon as I’m able to say something on the conclusion of the investigation, you will have a lot more on it.”
Asked why he should not resign like Matt Hancock as health secretary and Allegra Stratton as Downing Street press secretary, Mr Johnson said: “I’m getting on with the job that I was elected to do and discharge the mandate that I was given, and I’m proud of what we have been doing.”
In response to a suggestion that some people believe he is a liar, Mr Johnson said: “If you are talking about the statements I’ve made in the House of Commons, I was inadvertently … I was wrong and I’ve apologised for that.”
The Prime Minister also admitted more needed to be done on the cost of living.
He said: “I accept that those contributions from the taxpayer – because that’s what it is, taxpayers’ money – isn’t going to be enough immediately to cover everybody’s costs.”
Put to him that means the Government is not doing everything it can, Mr Johnson admitted: “There is more that we can do.
“But the crucial thing is to make sure we deal with the prices over the medium and long term.”
However, the Prime Minister also warned increasing state support beyond its current levels could drive inflation even higher.
There is a “global context” caused by a surge in energy prices, which is hitting all aspects of the economy including food, he said, adding: “The cost of chickens is crazy.”
The Prime Minister also struggled when given the case of a 77-year-old viewer called Elsie, who has seen her energy bill increase from £17 to £85 a month, has cut down to one meal a day and travels on buses all day to stay out of the house.
He responded: “I don’t want Elsie to cut back on anything.
“The 24-hour freedom bus pass was something that I actually introduced.
“What we want to do is make sure that we have people who are in particular hardship looked after by their councils, so we are putting much more money into local councils.”