The King's Speech won seven Baftas and Mr Swain's work was recognised in the acceptance speeches.
The Baftas will take place on 10 February, and the Oscars on 24 February.
Starring Dominic West, Appropriate Adult has already been honoured with TV Baftas, RTS and Broadcasting Guild Awards.
The winner of the EE Rising Star Award will be unveiled at the Baftas on 10 February.
Dame Thora picked up two of her three Baftas for her Talking Heads monologues, written by Alan Bennett.
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Clare Balding will receive a special award for outstanding achievement in factual presenting at this year's TV Baftas, organisers have announced.
Goffe has collected Baftas for children's animation Lost and Found (2009) and short animation Jojo In The Stars (2003).
Its Oscar success comes after it was named best animated feature film awards at the Baftas and the Golden Globes.
She was also nominated for the prestigious Richard Dimbleby Award for Best Television Presenter (Factual, Features and News) in the BAFTAS 2000.
Co-writer James Corden, who plays Gavin's best friend Smithy, also picked up the best comedy performance award at the Baftas in April.
Last week it was nominated for nine Baftas and eight Academy Awards.
The French are back with a strong presence this year, after The Artist dominated at both the Baftas and the Oscars in 2012.
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Lee has two best director Baftas already - one for Crouching Tiger, Hidden Dragon in 2001, and another for Brokeback Mountain in 2006.
He received his CBE back in 1956, after a triumphal appearance in Peter Brook's Hamlet in Moscow, and has also won several Baftas.
It was the first time that Strachan - who has presented children's shows for nearly 20 years - had triumphed at the Children's Baftas.
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But the Irishman's plans to lubricate his commentary box performance suffered a blow after he broke his ribs in a post-Baftas fall at his home.
Hollywood blockbuster Les Miserables - for which some scenes were also filmed in Winchester - was nominated for BAFTAs and Academy Awards for its costume design.
The Oscar-winning director picked up the outstanding British film award, for Bond's 23rd outing, alongside producers Michael G Wilson and Barbara Broccoli at this year's Baftas.
The BBC3 show beat the likes of Strictly Come Dancing and Britain's Got Talent to the audience award, voted for by the public, in this year's Baftas.
Williams, who celebrated his eightieth birthday in February, has - on top of his five Oscars - won four Golden Globes, seven Baftas and 21 Grammy awards.
Elsewhere at the BAFTAs, Brits dominated the main acting prizes.
The 50th anniversary of Doctor Who was marked at Sunday night's TV Baftas with a video montage while Jenna-Louise Coleman, who plays current assistant Clara Oswald, presented an award.
This year's Baftas ceremony will be hosted by Stephen Fry and broadcast on BBC One and BBC One HD, following a red carpet show on BBC Three presented by Edith Bowman.
Despite sweeping the boards at the Baftas on Sunday and being hotly tipped for Academy Awards success, Mr Swain said The King's Speech relied heavily on the goodwill of all those involved.
Chancellor's co-stars in The Hour - Dominic West and Romola Garai - are also nominated for Baftas for other shows, Appropriate Adult (Dominic West) and The Crimson Petal and the White (Romola Garai).
The controversy here has continued to increase now that Affleck and Argo have been on a serious hot streak, with both winning top honors at the BAFTAs, Golden Globes, Directors Guild Awards, and Producers Guild Awards.
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Norton has already picked up two Baftas, an International Emmy and a host of other awards for the show, earlier this year So Graham Norton was adapted to run each nightly as V Graham Norton on Channel 4.
The fact it focuses on real-life Hollywood producers saving the day probably has not done it any harm, and it has cleaned up at most major awards ceremonies so far, including the Baftas, Golden Globes, Producers Guild Awards and Directors Guild Awards.
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