If the Queen or the Archbishop of Canterbury wanted to, would they have the power to dissolve the Anglican Church
No.
since (correct me if I’m wrong here) they are the Heads of the Church of England?
There is no “head” of the Church of England (other than Christ). There is a Supreme Governor (of which Queen Elizabeth II is by virtue of being monarch) and there is Primate of All England–the Archbishop of Canterbury.
As in political matters, the Queen’s authority over the church is largely ceremonial. She doesn’t actually give orders to bishops. She does appoint high ranking church officials, but this is done on the advice of her Prime Minister (who in turn simply recommends the people nominated by the church itself).
The Archbishop of Canterbury is the closest thing to an actual leader the CofE has, but even his power is rather limited. Outside of his own diocese, if he wants to get anything done he has to do it through persuasion rather than by demanding obedience.
The real authority within the Church of England is held by the General Synod, which is a legislative body made up of bishops and deputies elected to represent clergymen and laypeople. However, even this body could not dissolve the Church of England.
As a state church, only the British Parliament could dissolve the CofE. More likely, however, they would simply disestablish it, breaking the links between church and state.
I guess the British government could cut the CofE off from the public trough, and probably will sooner than later.
The Church of England does not get funded by the government or by tax payers. Half of its incomes comes from gifts and donations from members. The rest comes from investment funds (largely property holdings donated over the centuries) and fees for Christenings, weddings and funerals.
Even if the CofE was separated from the state (assuming the government did not strip it of all its valuable property), the CofE would continue to be financially stable.
