* Rise in inflation is worrying, Cameron says
* June 22 budget will outline scale of deficit reduction
* Cameron: failing to deal with debt will kill recovery
(Edits, adds quotes on lending to businesses, bank levy)
By Estelle Shirbon
SALTAIRE, England, May 28 (Reuters) - The rise in British inflation has been worrying and the independent Bank of England will need to set interest rates to control it, Prime Minister David Cameron said on Friday.
In a speech later, Cameron said his government's plans to slash a record peacetime budget deficit over the next five years would enable interest rates to stay low for longer, save the economic recovery and ease inflationary pressures.
"Our budget deficit is set to overtake Greece," Cameron told business leaders in Saltaire, northern England. "If we don't deal with this, there will be no growth, there will be no recovery."
Cameron's concerns about rising inflation appear to contradict assurances from the Bank of England that a recent spike -- to nearly double the 2 percent target in April -- is temporary and will subside over the coming year.
"Policy set independently by the Bank of England, that is the right way to do things," Cameron told GMTV.
"We have seen a slightly worrying increase in inflation in recent months so interest rates will be set to control inflation."
Conservative leader Cameron, who became prime minister earlier this month after forming a coalition with the smaller Liberal Democrats, has been outspoken about monetary policy in the past -- an area usually avoided by government ministers.
At the Conservative conference in October 2009, Cameron, then in opposition, said "printing money leads to inflation". He was referring to the Bank of England's quantitative easing programme, under which it bought assets with newly created cash.
BANK LEVY
Earlier this week the OECD said the Bank should raise interest rates no later than the fourth quarter of 2010 due to the gradual drift up of some measures of inflation expectations.
However, if rates go up to contain inflationary pressures, analysts say there will be little to protect the still frail economy from sweeping government spending cuts.
The Office for National Statistics said this week the economy grew by 0.3 percent in the first quarter, up from an initial estimate of 0.2 percent.
In his first major speech since taking office, Cameron said the coalition's emergency budget on June 22 would outline how the deficit -- running close to 11 percent of gross domestic product -- would be dealt with over the next few years.
He warned that failing to take action now would kill off Britain's recovery from the worst recession since World War Two.
"Getting the deficit down and keeping it down will ... allow interest rates to remain lower for longer," he said.
The coalition has outlined this week an initial 6.2 billion pounds ($8.9 billion) of spending cuts this year.
Cameron also said he and his finance minister, George Osborne, would be pressing for an international agreement on some form of banking levy at meetings with their G20 counterparts in Korea and Canada in June.
"Given all the money that the public had to put into the banks, the idea of a modest bank levy going into the future makes sense," Cameron said.
"I'm pretty hopeful that other countries -- and speaking to the French and the Germans and listening to what (U.S.) President (Barack) Obama has said -- pretty hopeful that can happen."
Asked about the problems still faced by many British businesses in accessing credit to keep their operations running smoothly, Cameron said he was aware of the problem and it was "absolutely vital" for the government to help address it.
"We are looking specifically at loan guarantees and the existing government schemes and can we expand them. We are also looking at net lending agreements with banks and how they can work better," Cameron said. (Writing and additional reporting by Matt Falloon, Adrian Croft, Kylie MacLellan, Fiona Shaikh; Editing by Charles Dick)