In the medieval west, the title of Emperor carried with it implications of authority and privilege that superseded that of a king. It did not necessarily carry with it the connotation it often has now of ruling over many different peoples, or ruling over a large amount of territory. Emperors could exercise power over and above that exercised by ordinary rulers.

Cromwell brings this up because the title of Emperor had some important implications in the west for relations between the church on the temporal power. Emperors were understood to wield one of the "temporal sword" in contrast to the "spiritual sword" held by the Pope. The two swords, in concert, were held to insure good governance of church and society. How exactly you interpret this depends on your point of view. Roman Popes traditionally argued that the temporal sword was inferior to its spiritual counterpart, and that Popes could command temporal rulers. This is a lot of what underlies the Investiture Controversy between the Holy Roman Emperors and the Popes in the 11th and 12th centuries; Emperors tended to argue that they were at least equal to the pope. At different points, Popes deposed emperors, as Gregory VII did to Henry IV, and at least one pope, Benedict V, was deposed by Otto I. Both Pope and Emperor made claims to holding authority over governing the church and Christendom itself.

This is important for Thomas Cromwell and Henry VIII because the title of Emperor had specific consequences for church governance. Historically, there had been a role for Emperors to intervene in the affairs of the church. The basic argument was that an Emperor, as opposed to king, could govern the church within his own realm even in face of the opposition of the church. If Henry could claim he was an Emperor, he could legitimate his assertion to authority over the English church, authority he desperately needed to annul his marriage and remarry in order to produce a viable male heir. The Tudor dynasty had to make imperial claims to justify control over the church. This is why, for example, Elizabeth I is often depicted in imperial regalia with a closed crown: Tudor propagandists were reinforcing the idea that she had the power of an Emperor. They hung quite a lot of their argument on one story from the reign of Henry V. According to the story, when the Holy Roman Emperor Sigismund visited England, his vessel was greeted by English dignitaries who asked if he came as a friend, or as an Emperor. Friend, the Emperor replied. Therefore, the English claimed, Sigismund indicated that he did not have imperial privileges in England, so they logically devolved to the English kings.

The Tudors also appealed to the example of the earlier Emperors who had exercised power over the church. Constantine, after all, had called the Council of Nicaea, not the Pope, and secular rulers played an important role in the convening of the other ecumenical councils as well. These claims far outlived Henry, as John Jewel would continue to argue for the secular role in church affairs in the 1560s, well after Henry's death, though Jewel was more concerned with temporal involvement in the church more generally than with imperial claims.

Cromwell claimed the English king was an Emperor because it had important implications for this ongoing dispute with the Pope in the King's Great Matter to procure an annulment.

Readings

Christopher Haigh, English Reformations

Dale Hoak, Tudor Political Culture

John Jewel, Apology of the Church of England