The correct option is A Parliament
Even before her accession to the English throne Elizabeth was expected to marry and had no shortage of suitors. Once, queen, her prospective marriage became a matter of national importance and parliamentary debate because it was inseparable from the questions of who would succeed her on the throne and whether they would maintain the Protestant religion of the church established by the Elizabethan Settlement. Although she accepted in theory that it was her duty to provide an heir, Elizabeth had a deep-seated aversion to the idea of marriage and was loath to be advised concerning either matrimony or the succession. Both Houses of Parliament saw fit to petition her repeatedly on these issues despite her evasive answers and attempts to block discussion of all such prerogative ‘matters of state’. In the Commons this was taken to impugn freedom of speech; it remained a source of tension even after pressure on Elizabeth to marry had been eclipsed by the problem of how to exclude undesirable contenders such as the Catholic Mary Stuart, Queen of Scots, from taking the English throne. By refusing to name her heirs Elizabeth managed to manipulate the succession as a political tool throughout her reign, to the intense frustration of her counselors, but ultimately as an effective strategy of self-assertion at home and abroad. Hence, Option A is correct. Elizabeth herself did not wish for any heir. The Privy Council was founded in 1708, much after Elizabeth's death in 1603, hence these options are incorrect.