One fifth said the eurozone would not exist in its current 17-member form, while the majority put the possibility of a eurozone break-up at 30%-40%.
The poll also found that most economists expect UK interest rates to remain at 0.5% throughout next year.
It was conducted among 34 UK and European economists who regularly advise the Bank of England.
Of the 27 who responded, 25 forecast recession for Europe next year.
Growth in Europe has slowed in recent months as the eurozone debt crisis has forced governments to rein in spending and has undermined confidence in global financial markets.
The eurozone economy grew by 0.2% between July and September, while the 27 economies of the European Union grew collectively by 0.3%.
Politicians have attempted to resolve the crisis, including an agreement to forge closer ties between EU members, but markets have yet to be convinced the measures they have taken are sufficient.
The longer the debt crisis rumbles on, the more likely Europe will return to recession, economists believe.
The CBI business group said that 2012 could be the beginning of a more prosperous future if the "pain" of deficit reduction passed quickly.
In his New Year message, the CBI's John Cridland said the eurozone crisis posed a "significant threat" to the British economy, because 40% of UK exports were sold there.
Mr Cridland added that the faltering recovery and the continuing debt crisis were stark reminders of the need to rebalance Britain's economy away from household and government debt.BBC