The ONS said service sector output increased by 0.8% in January on a year earlier and was up 0.3% month-on-month, despite the snow impact at the start of the year.
It is hoped that this solid performance will offset woes in the construction and manufacturing sectors.
Increased demand for exports has been helping, boosted by the recent weakness of the pound, which makes it cheaper to buy British goods and services.
The BCC's survey showed improvements in both the manufacturing and services sectors, although employment had weakened.
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