How did Henry VIII ascend to the throne with so little opposition? After centuries of instability, it seems that everyone was happy with him. Was Henry VII’s reign really that successful?

I think the key answer to this in both cases they were seen and portrayed as a relief from their predecessors. And yes, that includes Henry VIII being a relief from his own father, as bizarre as it sounds for someone as infamous as Henry VIII being a relief from anyone.

After the chaos of what would later be called the Wars of the Roses, Henry VII presented a genuine opportunity for peace. It was what Edward IV had also attempted to. It was a necessary process for there to be a certain amount of forgiveness and mercy to be practised, in order to bring people on side and avoid endless blood feuds and rivalries. Of course, famously Henry VII's masterstroke in this strategy was marrying Elizabeth of York, uniting Yorkist and Lancastrian lines and the Tudor rose symbol was invented to promote this idea of unity, indeed while Lancastrian had sometimes used a gold rose the red Lancastrian rose was largely invented by Henry VII to match with Edward IV's white rose for the symbolism. Another helpful part of marrying Elizabeth of York was that it also gave more solidity to his fairly weak claim to the throne. The important context of Henry VII's accession was that after all the deaths in the Wars of Roses there were comparatively few claimants, with the main Lancastrian line wiped out and Edward and his sons dead. It was in the opening that Henry VII became a contender and not simply a distant relation, and it was the rift between Richard III and Elizabeth's mother the dowager queen Elizabeth Woodville that provided him the opportunity. Henry VII's mother Lady Margaret Beaufort was in contact with Elizabeth Woodville through a shared doctor, and it was with the dowager queen's support that Lady Margaret and Bishop John Morton organised a large part of both the Duke of Buckingham's rebellion and the later coup. It's conspicuously that in his little court in exile Henry was not only joined by Lancastrians like the Earl of Oxford but also member of the Woodville family like the queen's brother Edward Lord Scales. the marriage between Elizabeth and Henry had already been negotiated before the Battle of Bosworth and Henry had sworn an oath to make the marriage when he returned to England. Elizabeth Woodville and her daughters were trapped taking sanctuary in Westminter Abbey for a significant portion of Richard's reign, genuinely fearing that Richard might kill them, so her options must have seemed few when Lady Margaret contacted her.

It was in this context that Henry VII took the throne. And it's notable he wasn't the most warlike king. He had a bit of a go at France by what seems like almost obligation, but he had much more notable achievements in diplomacy and trade. Henry's closest advisors the now Cardinal John Morton and Bishop Richard Foxe were both known to be somewhat skeptical of war. Instead Henry became known for regulation and finance. As well as implementing restrictions on retainer designed to reduce civil uprising, he also enacted major taxation leading to the supposed "Morton fork" from the Cardinal, although the evidence on whether Morton ever said the quote attributed to him seems shaky. Furthermore, in response to the unrest, plotting and pretenders mentioned by u/mimicofmodes, Henry VII also began a major debt policy. He starting calling in hundreds of various debt claims, some spurious and some intentionally unreasonable. This was partially to restore crown finances as his tax policy was, but here it was also leverage against potential troublemakers. These debts were an excuse to keep an eye on people, to legally harass them, and if people stepped out of line they knew Henry could call in these debts, ruining their estates and impoverishing their families. A certain amount of corrupt money-making occurring off the back of this debt system by financial officers like Reynold Bray, Richard Empson and Edmund Dudley, who do also appear to have accepted bribes for other favours. Not new in this system, and the laws on corruption were shaky and unevenly enforced, but corruption does appear to have escalated. It was this environment of financial exaction, the politics of fear and the expansion of corruption that led Henry VIII's accession to be hailed. Not only did he remove some of more burdensome policies and claims, but he also executed Empson and Dudley, the most unpopular by that point. Furthermore, through his interest in jousting Henry had befriended certain Yorkist candidates for the throne, and their support helped ensure his accession. As mimic covered, that didn't always turn out given Henry VIII's later conflict with his former friends the Courtenay and Pole families. But it did help stabilise the succession.