The husband-and-wife team beat Christopher Coles and Sophie Brown 21-11 21-11 in the final in Derby.
It is the fourth occasion the top seeds have triumphed in the event overall, beating the record of Olympic silver medal-winning pair Nathan Robertson and Gail Emms, who won it three times.
Between them, the Adcocks have now won 10 English titles.
All five titles at the championships were won by the top seeds.
Rajiv Ouseph won his eighth men's singles title, beating Alex Lane 21-10 21-9, and in the women's final Fontaine Chapman triumphed after twice being a beaten finalist.  She beat training partner Chloe Birch 21-15 21-16.
In the men's doubles, Marcus Ellis and Christopher Langridge proved too strong for Peter Briggs and Tom Wolfenden with a 21-15 21-11 victory.
In the women's doubles, defending champions Heather Olver and Lauren Smith beat Brown and Kate Robertshaw in the closest final of the day, which ended 19-21 21-18 21-7.

Warren, 79, who started the Granada Television show when he was 24, died on 1 March after a short illness.
His coffin was carried into the cathedral by members of the cast, watched by the crowds outside.
Among those who attended the service were Julie Goodyear and William Roache, who has played Ken Barlow since the first episode in 1960.
Goodyear, famous for playing barmaid Bet Lynch, paid a heartfelt tribute to Warren, a friend of 50 years.
"We cried together and we laughed together," she said.
Canon Philip Barratt said all the hymns and readings at the funeral, which was also open to members of the public, were chosen by Warren.
"It's a big service for a very big character and a lovely part of the history of Manchester," he said.
Former stars in the congregation included Ken Morley, who played Reg Holdsworth, and Christopher Quinten, best known for his role as mechanic Brian Tilsley.
Warren was born Anthony McVay Simpson in Eccles, Salford, in 1937, and took the stage name of Warren during his career as a child star.
He trained at Liverpool's Elliott Clarke Theatre School and was a regular on the BBC radio show Children's Hour, before acting in radio plays alongside some of the actors who would became household names because of Coronation Street, including Violet Carson and Doris Speed.
His idea for the soap opera was commissioned for 13 episodes by Granada in 1960 and the show has gone on to be one of the UK's most successful ever, reaching viewing figures of 26.6 million for the departure of the much-loved character Hilda Ogden in 1987.
He wrote episodes for the ITV soap until the late 1970s and was made an MBE in 1994 for his services to television drama.
The writer remained a consultant on the soap until his death, with his creator credit appearing at the start of the closing credits of every episode.

Under a five-year plan released on Wednesday, the cost of stamps will also rise and as many as 8,000 jobs will be eliminated.
But the agency says it will also open more retail locations across Canada.
The service faces a projected 1bn Canadian dollar ($943m; Â£576m) loss by 2020 without "fundamental changes".
Canada Post lost C$73m in the third quarter of the current fiscal year, CBC News reported.
"Canadians expect Canada Post to continue to remain financially self-sufficient and not look to their hard-earned tax dollars for funding," the postal service said.
At the same time, "the rise in digital communications has dramatically changed the postal needs of Canadians".
Direct to the home delivery will be replaced by community post boxes installed throughout residential areas, Canada Post said in its plan.
The agency said two-thirds of Canadians, mostly in newer suburban neighbourhoods and rural areas, already receive their mail through this method.
The cost of postage stamps purchased in bulk will rise to $0.85 per stamp, up from $0.63 today, among other price rises.
In all, the plan will return the agency to financial sustainability by 2019, Canada Post said in a report, citing annual savings of up to C$900m.
Between 6,000 and 8,000 jobs will be eliminated as part of the plan - 12% of Canada Post's employees, although it says its workforce is ageing and it expects almost 15,000 workers will retire or leave the company in the next five years.
Canada Post delivers close to 10 billion letters and parcels each year but has seen a 24% drop in letters delivered since 2008.
Chris and Gabby Adcock won the English National Championships mixed doubles title for the third successive year.
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The funeral of Coronation Street creator and writer Tony Warren has taken place at Manchester Cathedral.
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Canada Post will phase out home delivery in urban areas over the next five years as the postal service struggles to rein in persistent losses.