Executions were part of everyday life in Tudor times, beheading was a dignified and honourable means of execution, as opposed to hanging which was shameful, maybe it was considered more important to medieval nobility than whether it was humane or not. Beheading was carried out using a sword in Europe, whereas the axe was more commonly used in England. Execution with a sword was performed with one single stroke and generally did a better job.
This form of execution in Britain was used as far back as Anglo-Saxon times, but was reintroduced during the reign of William the Conqueror. Waltheof, Earl of Northumberland, had his head taken off with a sword in 1076, the axe was commonly used at a later date. Hanging was the usual punishment for most crimes but down the centuries beheading was the norm for men convicted of treason along with the brutal punishment of drawing, hanging, and quartering. Women were hanged but also burnt at the stake. However, noble women often met their death on the 'block' Lady Jane Grey and Margaret Pole the Countess of Salisbury both ended their days this way.
Anne Boleyn, as mentioned, the date of execution was set for the 19th of May and she was sentenced to death by burning at the stake or beheading. To spare Anne the pain of a potentially messy execution by axe, something he didn't do for his kinswoman Margaret Pole, who died a terrible death at the hands of an inexperienced executioner, Henry granted a special dispensation, bringing over an expert French swordsman.
Before Anne died she said
"a more merciful prince was there never: and to me he was ever a good, a gentle and sovereign lord."
Anne's grave in the Chapel of St Peter ad Vincula was unmarked until the 19th century. Today her name is carved into the marble floor.
In the image is the Martyrdom of St. Margaret of Antioch in which she is executed with a sword.