Who was on the throne between 1554-1616?

No-one. Following the execution of King Charles II in 1649, England became a republic, known as The Commonwealth of England.

The head of this government was Oliver Cromwell, who took the title of Lord Protector.

Cromwell died in 1658 and was succeeded as Lord Protector by his son, Richard Cromwell.

On 29th May 1660 the monarchy was restored and Charles I's son became King as Charles II