The letter added that a downturn would affect the need for migrant workers, particularly in jobs such as construction where they make up a large proportion of the workforce.
"Increased public hostility to migrants" was predicted to result from heightened competition for employment.
The leaked letter stated: "There is a risk of a downturn increasing the appeal of far-right extremism and racism, which presents a threat as there is evidence that grievances based on experiencing racism are one of the factors that can lead to people becoming terrorists."
The letter also pointed out that a lack of resources could lead to some difficult choices in terms of police numbers and priorities.
There could be a reluctance by police authorities to increase funding for forces which could also be hit by high fuel costs and pay increases, it added.
However, the letter said a downturn may stop the alcohol industry cutting prices and this could lead to a decrease in drink-related violence in town centres.
Cocaine use would also be expected to fall as Britons' finances were stretched.
Mr McNulty told the BBC Radio 4 Today programme: "We've never made any pretence that the economy and crime are inextricably linked.
"This really is a statement of the blindingly obvious - people would be astonished if the Home Office weren't looking at how the relationship between crime and the criminal justice system and the economy interact and relate with each other.
"What the letter also says, albeit a draft, is that we are better placed now than we were with equivalent problems in the '70s and '90s to tackle them."
The Conservatives have seized on the document, saying it proved that the slowing economy would threaten people's security and safety.
Shadow home secretary Dominic Grieve said: "It is deeply disturbing that a department as shambolic as the Home Office already faces such problems as a result of the economic downturn. It is patently not equipped to cope. Why haven't they prepared for this?
It is appropriate that the Home Office considers the effects the economic climate may have on crime and other policy areas
Home Office spokesman
"Now we see that the consequences of Gordon Brown's complete mismanagement of the economy will not just hit hard-working families in the pocket but will also threaten their security and safety.
"Across the board Labour are failing in their duty to ensure the welfare of the British public."
BBC News political correspondent Gary O'Donoghue said that although it came as no surprise that ministers expected crime to rise in an economic downturn, there would be embarrassment that these thoughts have become public.
Professor Richard Garside, the director of the centre for crime and justice studies at King's College London, said there was a long-term correlation between economic and social processes and the level of crime.
"The document seems to imply this is going to raise significant challenges for the police and other criminal justice agencies in the next three to four years," he said.
"The question is, is it really going to be the criminal justice agencies which are going to solve this problem? The answer, I suspect, is no."
The Home Office said it was confident it had the right systems in place to respond flexibly to changing economic needs.
A spokesman said: "We do not normally comment on leaked documents but this is draft advice that the home secretary has not cleared and has not been sent to Number 10.
"It is however appropriate that the Home Office considers the effects the economic climate may have on crime and other policy areas."
The leak comes two days after Chancellor Alistair Darling said the UK was facing its worst economic crisis in 60 years.
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