According to The Severed Alliance they broke up before Christmas 1983. The New York trip referred to was The Smiths' first US show, New Year's Eve 1983/84. The anniversary edition has an additional indirect quote by Rourke, that makes it sound like it was because of another girl.
"A far more alarming absentee from The Smiths’ camp was Marr’s girlfriend, Angie Brown. The road crew was shocked to hear that she and Johnny had split up just before Christmas. According to Rourke, Marr had befriended another former flame, Tracy Donnelly, and it was now unclear what lay ahead. It was difficult to escape the feeling that an era of innocence had already passed."
The part about Tracy Donnelly is not in the original edition.
They apparently got back together in early 1984:
"The first month of 1984 was a time for putting lives back in order. Marr was still staying at Joe Moss’ house with Andrew Berry, and he spent many evenings mulling over the ‘Angie problem’. Moss had considerable respect for Angie’s strength of character and was categorical in his advice. 'I knew Angie really well. At one point, he tended to go against her, a young bloke, with a lot of attention. I told him the cool thing to do was to get married. What he needed was a strong woman, which she is, and 100 per cent behind him.' The pair were soon reunited but, meanwhile, there were Smiths-related matters to sort out too."
They eventually got married during the US leg of the Meat Is Murder tour in 1985.
Why did Angie and Johnny break up in 1983-4 ? Well ask Uncle Skinny mate! Ol'skinny set you rudder straight on that one ...sort of. It was ofcorse, Morrissey and Johnny was then an item ! Got it ? Moz attempted to move on from there...a ha ha ha.