The OED’s first citation for this adjective comes from the 1964 movie tie-in The Beatles in A Hard Day’s Night, by John Burke, and helpfully includes an etymology and partial definition: “‘I wouldn’t be seen dead in them. They’re dead grotty.’ Marshall stared. ‘Grotty?’ ‘Yeah—grotesque.’” The OED’s full definition: “Unpleasant, dirty, nasty, ugly, etc.: a general term of disapproval.”
A Google Ngram graph shows that grotty is a dead Britishism, with steadily increasing U.S. use. That appears to have picked up in recent years, including in a piece about the HBO series “Girls” in today’s Philadelphia Inquirer: “Hannah is still waiting hand in foot on Adam (Adam Driver) in his grotty apartment.”
An April 2012 New York Times theater review by Eric Grode says the play’s setting, in “a wood-paneled living room in Paterson, N.J., is more strip mall than Vegas Strip. (Mimi Lien contributed the suitably grotty set.)”
The reviewer’s name reminds me that there is more or less exact American equivalent, spelled, variously, grody, groaty, groady, and groddy, with all but the last rhyming with toady. The OED’s first cite for this is a 1965 Houston Chronicle but it gained immortality in the early ’80s, via Valley Girl Moon Unit Zappa and her immortal phrase “grody to the max.”
Is there any difference between grotty and grody? I leave a definite answer to wiser heads than mine, but I will note that all the OED definitions of grody refer to people and all but one of grotty refer to places.
notoneoffbritishisms.com 
“Grotty” is a well-established Australianism, prevalent for as long as I can remember (say, early 1970s) and still going strong.
I believe that “grotty” and “grody” come from Scotch Gàidhlig “grod”. meaning rotten, corrupt, or putrid. https://learngaelic.scot/dictionary/index.jsp?abairt=grod&slang=both&wholeword=false Irish gaelic has the word meaning nothing relevant.
I think more recently the word ‘grotty’ is often used when an individual is feeling a little bit ill or under the weather. EG, ‘Urgh, I feel a bit grotty today’.
As with the previous poster, grotty seems to have moved on from an adjective referring primarily to objects to one frequently used to describe people, particularly their mood or behaviour (such as “I’m feeling really grotty today”). It’s similar in usage to “shitty”
Thats how I always remember it being used. Im from England. My mum always said it when she was snotty or feeling run down. She would also often tell me to “shift that grotty thing outside” referring to to dead animals I’d bring home to taxidermy.
Don’t forget “grotsville” in common use in UK and USA
The first time I remember hearing this adjective was a line of Michael Caine’s in “Sleuth”, where he described the Laurence Olivier character’s idea as “a grotty little plot”. This was especially memorable with the character’s glottal stop, which rendered it as “A gro’y li’le plo’ “.
OT: Grotty, rhymes with dotty, used in a TV Guide article anticipating the season 3 premiere of /Downton Abbey/ here a week ago: “…the U.S. is once again poised to go dotty for /Downton/.” Google Ngram doesn’t indicate it as a NOOB, but does reveal interesting timelines for it on both sides of the pond.
I remember “The Fall and Rise of Reginald Perrin” and his fabulously successful “Grot” shops.
Any chance a finger slipped on the keyboard? O and I are right next to each other, and “gritty” sounds perfectly natural to my American ears in your “strip mall” citation.
Ben:
I’ve been using “grotty” for years. I can’t pin down a date – probably in the mid-eighties – and always referring bto things or a situation rather than people, mainly in the sense of tawdry, crappy, slimy, and chintzy.
“… hand in foot…”??? I believe that’s “hand and foot”.
I remember introducing the word ‘grotty’ to a young lady from the US when I was about 16 – so that’s over 30 years ago, folks. She was staying with us as part of a youth orchestra tour and we were both horn players. I remember finding it astonishing that she washed her hair every single day, while she found our vocabulary bizarre and amusing. She liked ‘grotty’, though she did call it ‘groty’ till we corrected her, and said she was going to use it when she got home.
“Grotty” wasn’t George Harrison’s coinage, not even Alun Owen’s for the Hard Day’s Night screenplay. It was part of George’s Liverpool street slang, as recorded by Frank Shaw in “Lern Yerself Scouse”, published about the same time as the film but based on research and lived experience over many years.
I see no one’s yet mentioned Fawlty Towers and the snobby customer who describes one of the main characters (Manuel? Basil?) as a “grotty little man.” So it is used to describe people, or at least was.
There also used to be a character called http://en.wikipedia.org/wiki/Grotbags on British children’s television, which sounds as if it was a derivation.
Yes! I loved grotbags. Good thing to call someone who pissdd you off too. She was hilarious!
I have tentatively concluded that by “a dead Britishism” you mean “a phrase that is dead British” rather than ” a British phrase that is dead”. But since “dead” (= “very”) is an adverb, it can’t qualify a noun like “Britishism”. Probably you were being playful, but I don’t think it quite worked.
I thought they meant it was dead as in no longer used. That confused me a bit. Yeah, it doesnt make sense. You can say dead good or dead busy, but dead Britishism sounds like its gone out of use. Using dead in that way often fails in print. Even “My mate is dead British” sounds only right said a certain way. It would still be met with jokes about how my mate is deceased even if they got what I meant.
My parents said grody since at least the 1970s in Texas.
Like Liverpool, from personal experience, grotty (adj) and grot (n) were in everyday use in Manchester the 1950s (can’t speak for anything earlier). Its derivation from grotesque is hard to believe (I think OED brings this from a Hard Day’s Night) because its meaning is the same as Scottish Gaelic ‘grot’ and is definitely not the same as grotesque.