He said he disagreed with the views expressed by FTSE 100 bosses in a letter published on Tuesday.
Heads of companies including BT, Marks & Spencer and Vodafone said an EU exit would deter investment in the UK.
But Mr Woodford argued it was very difficult to build a credible economic argument for the UK either staying in or leaving the union.
Rather, the debate was a political argument about issues such as immigration and sovereignty, he said.
The long-term economic implications may not be as extreme as some have suggested, but regardless of the outcome of the 23 June referendum the effect would be profound, according to the high-profile fund manager.
A vote to leave could also spark a crisis for the EU project, which Mr Woodford said was facing an array of challenges on a macro-economic and political level.
There were fundamental political differences between member states on a range of important issues, as well as an immigration crisis and a stagnant eurozone economy.
"ECB chief Mario Draghi is printing money and trying to do his bit, but the macro headwinds are intense and unemployment remains high. It is these problems that a UK exit could shine a brighter light on," Mr Woodford told the BBC.
He believed investors should be braced for more "extraordinary monetary policy" by the world's central banks, such as negative interest rates and negative yields on 10-year government bonds.
The global economy also faced a slowdown as well as the threat of deflation, while big problems remained in China, which was adjusting to cope with much slower economic growth.
Major FTSE 100 companies such as Shell, BP and HSBC would all be forced to cut their dividends this year amid continuing low oil prices and poor investment returns, Mr Woodford predicted.
On Tuesday, mining giant BHP Billiton said it was slashing its dividend, abandoning a long-held policy of maintaining or increasing payments to shareholders, reducing the payout from 62 US cents a share to just 16 cents.
Mr Woodford is considered in the industry as one of the UK's best-performing fund managers.
He rose to prominence during a 25-year career at Invesco Perpetual for taking a long-term view on investments.
One of the best-known examples of his strategy was refusing to invest in the dotcom boom of the late 1990s and early 2000s.
Last year he set up his own fund, Woodford Investment Management.

It is understood 150 people work at the office in Dundalk, County Louth.
eBay have not said how many staff will be impacted by the closure. It said it will begin a formal consultation with employees.
The company said the plant will close in the second quarter of 2017.
The closure comes after the decision to separate eBay and its PayPal business.
After the split, PayPal became landlords of the facility in Dundalk from which both companies have been based.
PayPal had told eBay that it intended to expand its business and asked tenants to leave so it could occupy the facility.
"We will begin a formal consultation process with our colleagues in Dundalk and will share any further information with them as a matter of priority," eBay said in a statement.
A spokesperson for PayPal said it was committed to its offices in Dundalk and Dublin.
"Today PayPal employs more than 2,600 teammates across both sites, and we're on track to reach 3,000 by 2018. The commitment is in line with our previous jobs announcements.
"Our operations will expand and move into the office space vacated by eBay."
Leaving the EU would not necessarily damage the UK economy, fund manager Neil Woodford has reiterated.
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Internet auction site eBay has told staff at an office in the Republic of Ireland that the facility will close next year.