The Upper House of the English parliament was the first - it was during the reign of Edward III that England began to move away from the model of European assemblies and develop a distinctive character of its own. It used to be said that the first representative Parliament in England was in January of 1265 when politician Simon de Montfort summoned it, packed it with his own supporters, and claimed legal and popular blessing for his cause. This is now discounted the title of a true Parliament for the reasons stated.
The Lords Spiritual and Temporal, who would eventually sit in a regulated and constitutional House of Lords, were originally the King's advisors. The clergy and the laity often had interests at odds with one another - it was one of the challenges of a sovereign in the Middle Ages to govern his realm without antagonizing this situation too much. There was an inequity in the positions of the two - while many Bishops (the Lords Spiritual) had vast temporal dominions, could put an army of men in the field, and could even excommunicate their opponents, it was held by the Church that temporal Lords had no business in the spiritual domain - not even the King. As for the commons, they at this time sat in the same assembly as the Lords Spiritual and Temporal, but their only real purpose was to assent to taxes at Royal request. Thus Parliament was a unicameral institution with the various estates of the realm sat together. This served the Medieval concept of government by assent of the commons, magnates and clergy well.
During the reign of Edward III, the Parliament split into two estates, and hence became a bicameral system. But, unlike other European nations, the English Houses of Parliament didn't split into three estates (clergy, aristocracy and commons), but only two, with the Lords Spiritual and Temporal sitting together. They remained in the original Parliament house, while the commons were moved elsewhere - they were not known as the House of Lords until the 16th Century. It was this house that first began to record its business and develop set ways of going about its business - this had been achieved at least by the assent of the first Tudor monarch, Henry VII.
While Parliament suffered under the Yorkists, it was to grow in strength and importance under the Tudors. It should be noted that the Houses at this time had no set meeting times - they could meet only when the King willed them to, but they were now his main method for authorizing taxation and legislating. We are seeing here the emergence of a uniform machinery of government - it is not as if beforehand the King could govern totally without the assent of his nobility. But now this assent was being embodied in Statutes and laws which carried weight. However, the King, as the executor, was not bound solely to Parliament's discretion. This relationship is known as "King-and-parliament."
In 1516, a judicial ruling destroyed any lingering idea that may remain that the Lords were two separate estates - it ruled that the Bishops and Abbots need not be present in the Lords for a bill to pass (absenteeism was rife in these early Parliaments.) Hence they were not a separate estate within the House, merely members of a House where decision was taken by majority vote with all members as equals.
Parliament became increasingly important throughout the 1530s when an unprecedented amount of legislation was passed at the instigation of Thomas Cromwell, as he took England through the revolution that was the English Reformation. As noted, it had long been held that Parliament could not interfere in religious matters, but this all changed with the Royal Supremacy and the Divorce Case. By going through Parliament, especially the Lords, Henry VIII ensured that an outward support of his powerful subjects was ensured. However, he was careful in the wording of the Acts that went through Parliament - they weren't making him the Supreme Head of the Church of England, it had always been so. Along with the backdating of Henry VII's reign so that all that fought against him at the Battle of Bosworth could be declared traitors, this was one of the great Orwellian coups of Tudor England.
What we now had was a "King-in-Parliament" as the sole sovereign authority in the realm. The Parliament was still open to his manipulation (or hers, in the case of Elizabeth I - during the Elizabethan Religious Settlement she put Bishops likely to vote against her in the Tower), and Lords hostile to a particular policy could perhaps be persuaded by threat or bribe to be absent from a particular vote. Parliament's power would grow and wane depending on the Monarch in it for some time yet.