To my knowledge, the prefix "Right Honourable" (usually abbreviated to "Rt Hon") is historically and traditionally accorded to all peers and peeresses of the third, fourth and fifth degrees, viz. Earl, Viscount, and Baron.
Members of Her Majesty's Most Honourable Privy Council - Privy Counsellors - are styled "Right Honourable".
If a peer is also a privy counsellor, the letters "PC" follow their title.
The Lord Mayors of London and York have been styled "The Right Honourable" since time immemorial.
Other lord mayors are so styled only when granted this privilege by The Sovereign: these are Belfast and Cardiff.
The Lord Provosts of Edinburgh and Glasgow are also styled "Right Honourable".
The remainder of lord mayors are styled "Right Worshipful".