LONDON (Reuters) - Business activity across the euro zone fell sharply last month as the bloc's dominant services sector joined the manufacturing sector in contracting, according to a survey which showed a broadbased decline.

HCOB's final composite Purchasing Managers' Index for the currency union, compiled by S&P Global and seen as a good gauge of overall economic health, sank to 48.3 in November from October's 50.0.

That was slightly ahead of a 48.1 preliminary estimate but still firmly below the 50 mark separating growth from contraction.

"The services sector, which had been holding up the overall economy, is now shrinking for the first time since January. This is bad news for overall growth prospects, especially since this weakness is seen across the top-three euro economies," said Cyrus de la Rubia, chief economist at Hamburg Commercial Bank.

A PMI covering the services industry fell last month to 49.5 from 51.6, its first sub-50 reading since January.

Suggesting no imminent turnaround, overall demand fell steeply, with the composite new business index dropping to 46.8 from 47.9, its lowest reading this year.

Despite that fall, services firms stepped up hiring, with the employment index rising to 51.0 from 50.3.

(Reporting by Jonathan Cable; Editing by Christina Fincher)