However, public borrowing figures also released on Friday showed that finance minister George Osborne has a lot of catching up to do to meet updated forecasts published earlier this month given the poor economic outlook.
The Office for National Statistics said services output grew 0.1 percent on the month in October, recovering from a 0.6 percent drop in September.
However, this is far behind the 1.2 percent growth that the sector enjoyed in the third quarter, which helped drive an overall 0.9 percent expansion in the economy as a whole in the three months to the end of September.
"It's not a great number but it is positive and it is better than the decline that had been expected," Ross Walker, an economist at Royal Bank of Scotland, said about October's services number.
"On the basis of all the published data it looks like the fourth quarter will be broadly flat, rather than negative."
Revised ONS figures published on Friday confirmed that third-quarter gross domestic product growth was the strongest since the third quarter of 2007. But much of that reflected a one-off boost from the London Olympics and a rebound from the second quarter when an extra public holiday dented output.
GDP in the third quarter was unchanged on the year, a small revision from the fall that the ONS had previously estimated.
The Bank of England and the government's forecasting body, the Office for Budget Responsibility, have both said a small quarterly contraction in the fourth quarter is likely.
Britain suffered its second recession since the financial crisis between late 2011 and mid-2012, and overall has recovered much more slowly since 2009 than most other big economies.
The BoE and other forecasters expect little in the way of a pick-up in the immediate future, given the weak global economy, government spending cuts and relatively high inflation.
"The economy faces a difficult-looking 2013 and we suspect it will only manage to eke out growth of 1.1 percent," said Howard Archer, economist at IHS Global Insight.
Recent ONS data has shown contraction in the retail and industrial sectors in the first part of the fourth quarter, though construction - which has been a major drag on GDP - appears to be stabilizing.
A GfK consumer confidence survey released earlier on Friday showed an unexpectedly sharp fall in morale.
Friday's GDP figures showed that the household savings ratio rose to 7.7 percent, its highest since the third quarter of 2009, suggesting an unwillingness to spend and a desire to pay down debts.
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One bright spot was third-quarter current account data, which showed Britain's deficit with the rest of the world narrowed more than expected to 12.8 billion pounds, equivalent to 3.3 percent of GDP, from 17.4 billion in the second quarter.
But Britain's government borrowed more than expected in November as government spending rose while a weak economy meant tax receipts fell compared to a year earlier.
Public sector net borrowing excluding financial sector interventions - the government's preferred measure - rose last month to 17.5 billion pounds from 16.3 billion in November 2011.
This was above economists' average forecast for 16.0 billion pounds and took borrowing in the fiscal year to date to 92.7 billion pounds, excluding the transfer of Royal Mail pension assets, up from 84.4 billion at the same point in 2011.
The OBR forecast earlier this month that the borrowing measure would reach 108.5 billion pounds this financial year, equivalent to 6.9 percent of GDP.
To meet this forecast, the deficit would have to fall 10.8 percent on the year, but so far in 2012, it is 9.9 percent higher than last year.
When the government came to power in 2010, it planned to largely eliminate the budget deficit by 2015 with spending cuts and tax rises. But a weak economy has since forced it to extend austerity until 2018.
(Reporting by David Milliken and Olesya Dmitracova; Editing by Ruth Pitchford)
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