The parliament is regularly to be summoned by the king's writ or letter, issued out of chancery by advice of the privy council, at least forty days before it begins to sit. It is a branch of the royal prerogative, that no parliament can be convened by it's own authority, or by the authority of any, except the king alone
It is one of the key elements of the British Constitution that a parliament can only be called on the authority of the reigning monarch. This very naturally creates a problem if there happens to be no reigning monarch at a particular point in time, and on two separate occasions it has proved to necessary to call a 'parliament' when the throne was vacant, namely;
These actions have been constitutionally justified on the grounds of expediency, as in;
this was for the necessity of the thing, which supersedes all law; for if they had not so met, it was morally impossible that the kingdom should have been settled in peace
Which is how William Blackstone was sought to explain the actions of 1660, comments which could equally apply to the circumstances of 1688.
Technically speaking such an assembly of the Lords and Commons was a Convention and not a Parliament (that is, simply an assembly of individuals with no constitutional powers) but in both cases the first thing these Conventions did, was pass an Act declaring themselves to be valid Parliaments notwithstanding the fact that they had not been formally summoned by royal writs in the first place. Since these Acts very naturally received the Royal Assent from those very monarchs that these Conventions supported, despite some occasional technical nit picking, no one has ever seriously doubted the legality of their actions.
By this means the British Constitution can pull itself up by its own bootstraps.
These Conventions that later declared themselves to be Parliaments are therefore generally known by historians as 'Convention Parliaments', specifically the;
Convention Parliament of 1660
Which was convened on the 25th April 1660, issued a declaration on the 8th May 1660 that Charles II was king "by inherent Birthright, and lawful and undoubted Succession", and was dissolved by the king on the 29th December 1660.
Convention Parliament of 1688
Which was convened on the 29th December 1688, resolved on the 28th January 1689 that James II had abdicated and that the throne was therefore vacant, and on the 6th February 1689 further resolved that the Prince and Princess of Orange should be made King and Queen, that is William and Mary. It was subsequently prorogued by the joint sovereigns on 27th January 1690 and was finally dissolved by royal proclamation on the 6th February 1690.
SOURCES
Charles Arnold Baker The Companion to British History (Longcross Press, 1996)
National Politics Website at
http://lego70.tripod.com/england/convention_parliament_1660.htm
http://lego70.tripod.com/england/convention_parliament_1688.htm
Blackstone, William Commentaries on the Laws of England: A Facsimile of the First Edition of 1765-1769 (Chicago: University of Chicago Press, 1979) from which quotations drawn
Text reproduced at http://press-pubs.uchicago.edu/founders/documents/a1_4_2s1.html | 
