In December, iPlayer attracted a record-breaking 187m monthly requests across all platforms, a 29% increase on the same month in 2010.
Top Gear's India special, which was recently branded as "tasteless" by Indian diplomats, was the most popular programme, attracting more than 1.7m requests after its transmission on December 28.
The motoring show was followed by Michael McIntyre's Comedy Show at over 1m requests, the EastEnders episodes on Boxing Day (966k requests) and Christmas Day (947,000), and Doctor Who's 'The Doctor, the Widow and the Wardrobe' (892,000).
Overall, the corporation's catch-up TV and video on-demand platform attracted 1.94bn TV and radio programme requests across all platforms in the whole of 2011.
However, December saw a big spike in people accessing the platform on connected TVs, mobile devices and tablet computers.
Last month, 7m programmes were requested on connected TV sets from brands such as Samsung and Sony, an increase of more than 1000% year-on-year.
Connected TV describes devices capable of delivering BBC iPlayer direct to TVs, including IPTV platforms such as BT Vision, connected "Smart TVs" and connected set-top boxes, such as Freeview HD, Freesat HD and some Blu-Ray players. Virgin Media on-demand figures are reported by the BBC separately.
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The BBC claimed that these figures reflect "both the growing penetration of internet-connected devices in the market, and the near-universal availability of BBC iPlayer on those devices".
BBC iPlayer registered its best ever week in the seven days after Christmas (December 26 to January 2), attracting 29.7m TV programme requests. This was primarily down to the estimated 6.8m iOS and Android devices activated on Christmas Day last year.
January 2 was the most popular day over the period, registering 5.4m TV programme requests over the 24-hour period, including 623,000 for the return of Sherlock.
"While 2011 was a remarkable year for BBC iPlayer across the board, the real story was growth of iPlayer on TVs, mobile phones, and tablets, outpacing PC growth many times over," said Daniel Danker, the BBC's general manager of programmes and on-demand.
"Having established itself as a must-have app for smartphone users and the gold-standard for TV on the go, we see huge potential for BBC iPlayer on the living room set in 2012 - the natural home for great TV - as audiences switch on to the benefits of connected TV."
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The Top 20 best performing TV programmes - December 20 to January 2 runs as follows:
1. Top Gear - India Special, December 28, BBC Two - 1,725,000 requests
2. Michael McIntyre's Christmas Comedy Roadshow, December 25, BBC One - 1,025,000
3. EastEnders, December 26, BBC One - 966,000
4. EastEnders, December 25, BBC One - 947,000
5. Doctor Who 'The Doctor, the Widow and the Wardrobe', December 25, BBC One - 892,000
6. EastEnders, December 27, BBC One - 884,759
7. EastEnders, January 1, BBC One - 865,000
8. Sherlock Series Two 'A Scandal in Belgravia', BBC One - 808,000
9. Absolutely Fabulous 'Identity', December 25, BBC One - 725,000
10. EastEnders, December 30, BBC One - 684,000
11. EastEnders, December 29, BBC One - 674,734
12. Great Expectations Episode One, BBC One - 642,000
13. EastEnders, December 22, BBC One - 608,000
14. EastEnders, December 20, BBC One - 596,000
15. EastEnders, December 24, BBC One - 587,000
16. Outnumbered Christmas Special 2011, December 24, BBC One - 572,000
17. EastEnders, December 23, BBC One - 560,000
18. Merlin Series Four 'The Sword in the Stone: Part Two, BBC One - 550,000
19. Great Expectations Episode Two, BBC One - 542,000
20. Tamara Drewe, December 23, BBC Two - 499,000