The UK will be affected by the euro area whether it votes to stay in or leave the EU, according to former Bank of England boss Mervyn King.
Lord King said the eurozone would still be the UK's biggest trade partner, even though the euro had been a "mistake".
Leave campaigners argue the UK could strike better deals with faster-growing countries if it were outside the EU.
However, Germany's finance minister warned the world economy would be "poisoned" if the UK departed.
British voters will be asked whether the UK should remain an EU member in a referendum on Thursday 23 June.
Asked if the UK would be badly affected by eurozone troubles after the referendum, Lord King told the BBC's Andrew Marr Show: "That will be true, in or out."
The life peer was governor of the UK's central bank during the financial crisis and stepped down in 2013.
He said the euro project had been a "mistake" and that Germany, one of the driving forces behind the single currency, could be better off leaving.
The "economic arithmetic" does not add up for the euro, but Germany and other EU leaders are supporting it for political reasons, he said.
"That is why in the longer run the euro area, not the EU but the euro area, is something that we should all be concerned about," he said.
Lord King would not comment on whether he was in favour of the UK leaving the European Union.
The UK sold £200.4bn of exports to eurozone countries in 2014, which was 39% of all the goods and services it sold abroad that year, according to the Office for National Statistics.
Of the EU's 28 countries, 19 use the euro.
Campaigners on both sides of the EU referendum are focusing on how the vote will affect British trade.
Speaking on the same show, London Mayor Boris Johnson said the "riskier option" was to stay inside the EU because its focus was on preserving the eurozone.
German finance minister Wolfgang Schaeuble conceded that the UK could negotiate a new trade deal to stay inside the single market – a free trade zone across all 28 EU countries – without being a member of the EU.
However, he said, a UK decision to leave would cause "years of the most difficult negotiations".
"For years we would have such insecurity it would be a poison to the economy in the UK, the European continent and the global economy as well," Mr Schaeuble said on the show.