In British English, the phrase a box of frogs has been colloquially used to express a great variety of notions, in particular ugliness (as in (as) ugly as a box of frogs) and madness (as in (as) mad as a box of frogs), but also unpleasantness, unpredictableness, agitation, disturbance, etc.

The earliest occurrences of the British-English phrase a box of frogs that I have found are as follows, in chronological order:

1-: From the following advertisement, published in The Star Green ’un (Sheffield, Yorkshire, England) of Saturday 8^th August 1970 [No. 26,037, page 2, column 3]:

Arbourthorne Hotel
(for a groovy weekend)
TONIGHT The fantastic
CASTLE CIRCUS
SUNDAY Recording stars
CAMELOT

Shake your lettuce up the spout,
Get that funky feeling;
Groove just like a box of frogs,
And strobe upon the ceiling.

2-: From a review of the gig that a rock band called Darts performed at Peppers in Cleethorpes on Thursday 6^th November 1980—review by ‘R. G.’, published in the Scunthorpe Evening Telegraph (Scunthorpe, Lincolnshire, England) of Saturday 8^th November 1980 [No. 28,364; Weekend Special!: page IV, column 2]:

Rita Ray, whose legs shone more than a Guardsman’s toecap, showed that strength of voice reminiscent of Tina Turner, while at the other extreme, Kenny Andrews boomed deeper than a box of frogs.

3-: From Going on safari… and off the map, by Alf Bennett, published in the Liverpool Echo (Liverpool, Merseyside, England) of Thursday 25^th November 1982 [No. 31,919, page 13, column 4]:

The name of Marrakesh means “walk quickly” in Arabic and was originally a warning to approaching caravans to get a move on before they were hijacked by marauding bandits. It’s as well to be aware that the descendants of those bandits are still around in the shape of highly-talented pick-pockets!
But that is a minor quibble with a city that is more fun than a box of frogs. Framed by the snow-capped peaks of the High Atlas Mountains, just a few spectacular hours drive away, it sports the wide, straight boulevards of the modern day.

4-: From Another legend lives, by Peter Holt, published in The Standard (London, England) of Thursday 5^th January 1984 [page 21, column 3]:

JEFF BECK has been secretly recording a new album with original members of his legendary Sixties R & B band, The Yardbirds.
The band is being produced by Paul Samwell-Smith […]
[…]
“We’re not re-forming under the name of The Yardbirds,” Paul tells me. “We felt that would be stepping back 20 years […].”
“We’re calling ourselves Box Of Frogs—we’re a pretty ugly bunch of characters after all.”

5-: From Your guide to films on TV, published in the Derby Evening Telegraph (Derby, Derbyshire, England) of Saturday 14^th April 1984 [No. 32,018, page 15, column 6]:

Fear in the Night (1972—ITV, 11.30): Hammer made something of a departure with this psychological box of frogs in which a woman newly-recovered from a nervous breakdown is deluded into committing a murder. Judy Geeson stars

6-: From the television programme guide, by Brian Hancill, published in the Daily Post (Liverpool, Merseyside, England) of Friday 19^th December 1986 [page 2, column 1]:

BBC 1
[…]
3.20 BOX CLEVER. Emlyn Hughes hosts the computerised quiz game that’s about as clever as a box of frogs.

7-: From Charles, [by Flan?], a comic strip published in the Sandwell Evening Mail (West Bromwich, West Midlands, England) of Wednesday 29^th April 1987 [page 18, column 6]:

MAUD’S PARENTS ARE VISITING. HER DAD’S A REALLY NICE CHARACTER, UNLIKE HER MUM
SHE’S GOT A FACE LIKE A BOX OF FROGS & A TEMPER LIKE A MALAYAN PIT VIPER ON A BAD DAY YET HE SEEMS HAPPY ENOUGH

8-: From Tom’s eye view of Scouse, by Tom O’Connor, published in the Liverpool Echo (Liverpool, Merseyside, England) of Thursday 22^nd October 1987 [No. 33,412, page 6, column 3]:

After a hard night on the ale, when the brain sends a message to one eye to open up and take a look at what’s going on, Scousers have their own term for a hangover. “Me head,” we say, “was goin’ like a box of frogs.”

9-: From It’s the age of the lie—honestly, by Lynne Curry, published in the Evening Post (Nottingham, Nottinghamshire, England) of Thursday 6^th October 1988 [No. 34,234, page 4, column 7]:

Birthdays lose their lustre when you’re older. They cease to be happy occasions and become grim reminders that you’re too old to be forgiven for being sick on chocolate, carving your name on the wall by the bus stop or pushing for the front seat on the top of a bus.
Somebody I know celebrated his 40^th a while ago and reluctantly went out for a meal. Then he had a face like a box of frogs throughout and wrecked the whole night.

10-: From Looking at life down at the pool, by Julie Nightingale, published in the Evening Post (Nottingham, Nottinghamshire, England) of Thursday 16^th August 1990 [No. 34,803, page 4, column 7]:

You’re losing your hair, you’ve got a beer gut that casts a shadow over your feet, you’re about as fit as Giant Haystacks and, let’s face it, you’re ugly as a box of frogs.

11-: From Frog-face role keeps versatile Jean busy, by Lynda Mitchell, published in the Kent Messenger (Maidstone, Kent, England) of Friday 10^th May 1991 [page 18, column 2]:

BROADCASTER and actress Jean Challis plays an unattractive character in Last Tango in Whitby, Mike Harding’s touching comedy about an elderly couple who find romance during their club’s annual stay at the seaside resort.
Jean, who presented BBC Radio’s Family Favourites programme for 10 years, said of her character Kathleen: “She is very repressed; she is described as the fat one with a face like a box of frogs.”

12-: From TV plus: Pick of the week, by David Richards, published in the Weekend Echo (Cardiff, Glamorgan, Wales) of Saturday 11^th January 1992 [page 20, column 5]:

THURSDAY 16 JANUARY
PERPETUAL MOTION: (BBC2 8.30pm) “It’s as ugly as a box of frogs” … “A million loose rivets flying in formation” … “It’s got Rolls-Royce engines and leather seats. What more could you ask for?” The subject of these comments is the Avro Shackleton, scheduled for scrapping in 1970 but given a 19-year reprieve when its replacement, the hi-tech Nimrod radar plane, failed to perform.

13-: From Videoview, by Alf Bennett, published in the Liverpool Echo (Liverpool, Merseyside, England) of Saturday 5^th September 1992 [No. 34,924, page 23, column 5]:

DANNY Glover, as one half of the Lethal Weapon team, is used to a livewire partner.
But in the video Pure Luck—out on September 18 from CIC—for Mel Gibson read Martin Short.
And while Mel is a hunk with a madcap streak, Martin is a different box of frogs altogether.

Note: The phrase a different box of frogs also occurred in Australian English, in the following from Tharunka (Kensington, New South Wales, Australia) of Tuesday 4^th June 1996 [Vol. 42, No. 7, page 37, column 3]—Tharunka is the student newspaper of the University of New South Wales:

PEEL at Iron Duke Hotel
15/5/96.
The Iron Duke Hotel in Alexandria has proven to be one of the better newer venues that have cropped up in Sydney over the last couple of years, booking a wide variety of bands ranging from hardcore punk to acoustic pop. On offer on this fairly laid-back Wednesday night were 3-piece band Peel, who are fairly well established now and known to some Uni audiences, and in support a band called Plunge.
One hastens to say that one was not amused by Plunge. […] One wishes that Plunge would do something to live up to their name, preferably from a great height.
Peel, thankfully, are a very different box of frogs.