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Amey said that currency devaluation, accompanied by higher inflation, would be the most effective way for the U.K. to recover from its "worst recession in 50 years".
"Lower sterling should hold up nominal GDP, which is as low as it has been for decades," he wrote in Pimco's long-term outlook report, which was published this month.
According to the Office for National Statistics' second estimate, U.K. GDP grew by 0.3 percent in the first quarter of 2013, with consumer spending and stockbuilding the main contributors to growth. In comparison, the economy contracted by 0.3 percent in the final quarter of last year.
Amey said Carney should aim to depreciate the pound by 10-to-15 percent against the dollar, taking it from around $1.50 to $1.37. So far, the pound has fallen 7.2 percent year-to-date against the dollar.
"I do not think it is a big ask, on the secular horizon. It is easy to depreciate the currency as the U.K. economy is relatively open, and it is small, so depreciation has less effect on the global economy," he said.
Exports constitute around 30 percent of U.K. GDP, with about half of all exports bound for Europe, although this proportion is decreasing.
The pound has gained 5.8 percent versus the euro this year, but Amey said it would be unviable to soften the pound against the single currency.
"In practice, we have to devalue against the non-euro currencies, i.e. the dollar and developing market currencies — currencies from those countries which do not have deficit problems, or have already worked through them," he said.
Amey added that Carney might also choose to increase the Bank of England's asset purchasing program. At its last meeting, the Bank kept the size of its purchases unchanged at 375 billion pounds ($584 billion), and maintained benchmark interest rates at 0.5 percent.
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However, Amey warned investors should steer clear of purchasing risk assets on the presumption of more quantitative easing.
"Financial repression, protection of real purchasing power, and tail risks of accelerated currency weakness, will likely dominate U.K. markets," said Amey, in his latest country report, published on Wednesday.
Efforts to boost nominal growth will remain hampered by the U.K.'s need to cut its budget deficit, said Amey, which he forecast will stand at 7.5 percent in 2013, excluding one-off items.
"The successful stabilization of private sector balance sheets has been achieved at the expense of public sector balance sheets," he said in Wednesday's news conference.
Pimco's Bill Gross, the manager of the world's biggest bond fund, has previously criticized the U.K.'s attempts to cut its deficit in the face of a weak economy.
"The U.K., and almost all of Europe, has erred in terms of believing that austerity, fiscal austerity in the short-term, is the way to produce real growth. It is not," Gross told the Financial Times last month.
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—By CNBC's Katy Barnato