The Office for National Statistics revealed the marginal services sector expansion as it revised down its figure for GDP growth in the third quarter from 1% to 0.9%.
This still-strong growth in the third quarter was aided by the London 2012 Olympics.
It also reflected the fact activity had been depressed in the second quarter by the Queen's Diamond Jubilee holiday.
Vicky Redwood, chief UK economist at consultancy Capital Economics, said: "GDP is still estimated to have risen strongly in Q3, but we already have plenty of evidence to suggest the economy may have contracted in the fourth quarter.
"Indeed, the UK could already be in a 'triple-dip'. We think the economy will struggle to grow by a meaningful amount next year."
The UK's recovery from its deep recession of 2008/09 proved short-lived. It contracted in three consecutive quarters to June this year, before rebounding in the three months to September.
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "It currently looks touch and go as to whether the economy can avoid renewed contraction in the fourth quarter as it faces the unwinding of the Olympics boost.
"News that service sector output only edged up 0.1% month-on-month in October reinforces belief the economy is having a difficult fourth quarter, but at least services output was marginally positive."
He added: "While it really makes little difference whether the economy grows marginally in the fourth quarter, is flat or contracts marginally, it would be good for confidence if the economy could avoid a GDP decline and avert headlines of a 'triple dip'."