If we assume this accident had a huge affect on his overall personality (and I am of the camp that the real shift in Henry VIII is more 1533, the loss of the Pope as a "higher figure" to him and the final step towards consistent instant gratification in his life in a way he had been working towards for years), then we possibly see Anne Boleyn remain around for at least a few more years, depending on her fertility and age (again, 1501 v. 1507). Should she not produce an heir over the next 3 years or so, I can definitely see their marriage beig annulled for the same reason he ostensibly got rid of Katherine for, but privately so that he is not embarrassed. Jane held out on him OTL based around the assumption he'd remove Anne, but should we understand his agreement with the evidence Cromwell collected was based partially on his own mental reaction to the physical pain he was in, we might assume that, even if he initially orders an investigation, Anne begging for her life may prevent that from going through. They'd weathered rough patches before, he had recently helped engineer recognition from Chaupys for her I believe, so it's entirely possible she escapes that plot unharmed. Let's say another stillborn in 1537, no pregnancies following, and an easy annulment with Anne keeping her own title as Marquis of Pembroke and Elizabeth remaining legitimate, as that's probably the one point she sticks to. Maybe that's her reward for easily stepping aside. Anne never remarries and, let's say, lives at least into her 60's.
Now Henry has the opportunity to remarry. By 1538/1539, Jane Seymour is definitely 30 and maybe, with Anne no longer around to annoy him, Henry won't find her quiet passivity so enthralling. OTL, he definitely tired of her almost immediately, so let's say she's managed to annoy him just enough that he sends her off home. Instead, let's say he goes for a foreign match again. Maria of Portugal definitely still says no, as do most Hapsburg related candidates (even if Christina of Denmark has no reason to fear for her neck, she probably doesn't want to marry a man that much older than her if she can help it). I could see him trying for Marguerite,
Princess of France, or maybe even ending up with Anne of Cleves again. Let's say Francis agrees to a match between his daughter and Henry, with Elizabeth once again being betrothed to Charles,
Duke of Orleans. Marguerite shows up, they have 1-2 surviving children, and Henry gets a son.
Now comes the interesting part. Does he die in 1547?
On one hand, Henry VIII not having that accident prevents him from giving up on all the exercise he was doing up until that point. He probably eventually gives it up after other injuries, but slowly and more in fits as he had already been doing. Thus, we probably see his weight increase much slower, and that'll extend his life a few more years. But, even with a slower climb to obesity and no major injuries draining him of his vitality, he's still a man with an incredibly indulgent lifestyle who never really learnt to pace himself. So let's say he lives to about 1551 and dies at 60.
His way of dealing with marriages for his children probably doesn't change. Mary is too dangerous, Elizabeth is young enough that it doesn't really matter until the end of his life, and even if she has a brief and unfruitful marriage to the
Duke of Orleans (she's 12 when he dies, she probably isn't getting pregnant and hopefully doesn't even get bedded), he really doesn't have a need to marry her off. Maybe, just maybe, she's married off to a useful ally in Scotland to try and secure the marriage of Henry's ATL son to Mary,
Queen of Scots. MAYBE she's even married to Marie of Guise's son in France for a second brief, probably unfruitful marriage. If Henry is smart about it, she may even be on the way to marry Philip,
Prince of Asturias as his second wife around her father's death. But let's saw she's unmarried and the responsibility of her stepmother, barely a decade her senior and probably interested in finding her a French husband.
Here's my family tree just based off these ideas:
Henry VIII,
King of England and Ireland (b.1491: d.1551) m. Catherine,
Infanta of Aragon and Castile (b.1485: d.1536) (a) -annulled 1532-, Anne Boleyn,
Marquis of Pembroke (b.1501/1507: d.1569) (b) -annulled 1538-, Marguerite de Valois,
Princess of France (b.1523: d.1574) (c)
1a) Stillborn Daughter (c.1510)
2a) Henry Tudor, Prince of Wales (b.1511: d.1511)
3a) Henry Tudor, Prince of Wales (b.1513: d.1513)
4a) Henry Tudor, Prince of Wales (b.1515: d.1515)
5a) Mary Tudor (b.1516: d.1558)
6a) Stillborn Daughter (c.1518)
7b) Elizabeth Tudor, Princess of England and Ireland (b.1533) m. Charles de Valois, Duke of Orleans (b.1524: d.1545) (a)
8b) Stillborn Son (c.1534)
9b) Miscarriage (c.1536)
10b) Stillborn Son (c.1538)
11b) Miscarriage (c.1538)
12c) Miscarriage (c.1540)
13c) Edward VI, King of England and Ireland (b.1541)
14c) Margaret Tudor, Princess of England and Ireland (b.1542: d.1542)
15c) Edmund Tudor, Duke of York (b.1544)
16c) Stillborn Daughter (c.1546)