In England, Westminster Abbey is where royal coronations and weddings are carried out and is known as a "Royal Particular" church, which is not part of a diocese but directly accountable to the crown. It has taken on the role of being the church where many of the royal acts of state including the coronation ceremonies of the sovereign.
Meanwhile, Canterbury has long been the seat of the Archbishop of Canterbury, who currently is the head of the Anglican Church. During the times when England was loyal to Rome, the Archbishop was at times a Cardinal, as well as a member of the Kings council, in roles as varied as treasurer and Lord Chancellor. Their power and authority gave great sway and was the seat of such notable men as Thomas Beckett, Thomas Cranmer, and Reginald Pole.
Is there any particular reason why Westminster is the church most used for royal functions instead of Canterbury, considering it's historical legacy as the seat of religious authority?
Is it merely because it's 70 miles away and Westminster is right in the city of London?
We must remember that the middle ages didn’t have quite the same conception of Church and State as we do. Instead of the State bearing secular power and the Church bearing religious power, both institutions had religious power. The State is tasked with carrying out God’s will in the physical realm; the Church is tasked with carrying out God’s will in the spiritual realm. And just as Canterbury Cathedral is the seat of the Church in England's (later the Church of England's) divine authority, Westminster Abbey came to be the paramount site of the English monarchy’s divine authority. This was largely thanks to the legacy of the English monarch who first built the Abbey - Edward the Confessor.
In the Anglo-Saxon period, there was no fixed site for coronations. Edgar, the first king for whom we have a detailed account of the ceremony, was crowned in 973 in Bath Abbey, and several others were crowned at Kingston-upon-Thames. Edward himself was crowned at Winchester Cathedral. But after his death, his short-lived successor Harold Godwinson decided to do the deed in Edward’s church, and William the Conqueror followed suit. As Roy Strong says in his Coronation: A History of Kingship and the British Monarchy, “William's decision to be crowned there must have been conditioned by a desire to cancel out Harold II's Coronation and also to be seen to be crowned in the burial church of the Confessor as his rightful heir. It was a precedent which, once established, proved permanent.” And once Edward the Confessor was canonized in 1161, this precedent became even more important. Now the English monarchy had its very own saint, who would doubtless intercede mightily to heaven against a Church that tried to meddle with the prerogatives of royalty.
Looking at the texts of the various editions of the Coronation ceremony, we can see that the editors make Edward’s name pop up wherever they can. The Sovereign is crowned with a crown called “St. Edward’s Crown” (though even if the original was connected with Edward, it was destroyed during the Revolution and the present version was made for the coronation of Charles II in 1661). The Sovereign sits in “King Edward’s Chair” when he is crowned. The Sovereign’s Ring, while not named for the saint, is said to have been miraculously given to him by St. John the Evangelist. In some older versions, the Sceptre and Robes are named for Edward. The Sovereign takes bread and wine for the Communion from St. Edward’s Chapel, where the relics of the saint were enshrined, and lays his regalia on the chapel altar when the coronation has concluded. Until the Glorious Revolution, the Coronation Oath contained a reference to “the glorious King St. Edward your predecessor.”
So, while I'm sure the Abbey's proximity to London is a helpful bonus, the primary reason (especially when it comes to the Coronation) is the desire to identify the present monarch with St. Edward the Confessor, an identification which would be shorn of much power if the ceremony occurred anywhere else.