Edward I was on a crusade from 1271 to 1274. If he dies during that periode in the crusade, then depending on the date, we have different possible successors.
Here is the order of succession of Edward I, taking the possible period of his death into account. I went up to the first male descendant of John Lackland.
1.Henry, Prince of England - The eldest living son of Edward I in 1271. He is only 3 and died in 1274 OTL. So, short reign under regency...
2.Alphonso, Prince of England - A son born to Edward I in 1273. If Edward I doesn't die before his birth, Alphonso will succeed is brother Henry, under a regency that is. Still, Alphonso died in 1284 OTL... So, a longer reign but a regency all the way.
3.Eleanor, Princess of England - Edward I's eldest living daughter who was born in 1269. At Henry's death, she is 5, which places her for ten years under Regency. At Alphonso's, she would be 15, making her major.
The fact she is a girl will be a disadvantage for her, but I believe she can take the crown. After all, she is the daughter of Edward I, who is a great grandson of Henry II who got the rights to the English crown from his mother Empress Mathidla, daughter of King Henry I.
4.Joan, Princess of England - A daughter born to Edward I in 1272. She has practically no chance of getting the crown though...
5.Edmund Crouchback - Edward I's only brother who is 26 in 1271. However, Edmund has no children yet at the time. He did sire 4 children OTL, but the eldest was born in 1278. Edmund can pretend to the crown or the Regency if he doesn't die in the Crusade.
6.Margaret, Queen of Scotland - Henry III's eldest daughter and a sister to Edward I. She is a 31 year old woman, married to King Alexander III of Scotland with whom she had three children.
7.Alexander, prince of Scotland - Margaret's eldest son. He is 8 but he died in 1283.
8.David, prince of Scotland - Magaret's second son. He was born in 1272 but died in 1281.
9.Margaret, Princess of Scotland - The only daughter of Margaret and Alexander III of Scotland. She was born in 1260 and married King Eirik II of Norway but died in 1283.
10.Beatrice de Dreux - Henry III's second daughter. She is a 29 year old woman married to John II, Duke of Brittany.
11.Arthur II, Duke of Brittany - Eldest son of Beatrice de Dreux. He is 9 in 1271.
12.John of Britanny, Earl of Richmond - Second son of Beatrice de Dreux. He is 5 in 1271.
13.Pierre, Viscount de Leon - Third son of Beatrice de Dreux. He is 2 in 1271.
14.Marie of Britanny - Eldest daughter of Beatrice de Dreux. She is 3 in 1271.
15.Blanche of Britanny - Second daughter of Beatrice de Dreux who was born in 1271.
16.Eleonore of Britanny - Third daughter of Beatrice de Dreux, born in 1274.
17.Richard, 1st Earl of Cornwall - Edward I's uncle as he is Henry III's brother. He is 62 in 1271 and died in 1272 OTL. He has two sons to suceed him.
18.Edmund, 2nd Earl of Cornwall - The eldest son of Richard of Cornwall. He is 22 in 1271 but died without children in 1300.
19.Richard of Cornwall - Second son of Richard, Earl of Cornwall. He is 19 in 1271, died in 1296 OTL but had children.