The 5th of November was an officially mandated holiday, as of the Observance of 5th November Act passed in 1606, and which remained until it was repealed by the Anniversary Days Observance Act 1859, as part of the then-government's drive to rehabilitate British Catholics following the Roman Catholic Relief Act 1829 and the Liberty of Religious Worship Act 1855.

In the militantly Protestant political landscape of 1605 and 1606, however, mandating the continued celebration of the 5th of November makes perfect sense. Indeed, the act was popularly known as the Thanksgiving Act. After all, the bonfires celebrate the thwarting of the Catholic plot to murder James I and Parliament. The continued celebration of the defeat of that plot served not only to stoke popular anti-Catholic and anti-Spanish sentiment as a means of building a Protestant English national identity centred around loyalty to King and Parliament, but also to subtly underline the effectiveness of the security forces to potential subversive elements.

"Allow" is a very strange way to put it. "Actively encourage through law" would be more accurate. Arguably, with great irony, Robert's Catesby's plot to blow up parliament with the King inside was the best thing that happened to James during the so-called "Blessed Parliament" of 1604 to 1610. It became a massive propaganda victory after James had been recently stung by unexpected difficulties in the previous sessions which led to a prorogation.

As I answer this I will be explaining some things about the historical Parliament of England, and other aspects of the context as they are necessary.

Firstly, it must be considered that the voting franchise of the time was around 2-3% of the country's population. Which meant that in individual counties, and especially in boroughs, the voting-rank population might be a few hundred or less. While some seats had a reasonable population of voters and more open rules on voting (the locals having some say on election rules) others were specifically decided by less than ten (this is mentioned in Penry Williams' "The Later Tudors": 1998 and Roger Lockyer's Tudor and Stuart Britain: 1485-1714: Third Edition 2005). It was also common practise to settle elections by negotiation, rather than public election campaigning which was seen as unseemly. So although there were no parties, it was common- especially as the 16th century rolled on and parliament grew more rowdy- for the Crown to negotiate through agents and friends to build a "court party" for a reliable base in the Commons. However for the elections of 1604 where members were assembled in March for the rest of the parliament, this activity was relatively lax on the part of the Crown which did not expect as much opposition. They spent the rest of the 23 sittings (full list of all 26 is viewable here:https://www.historyofparliamentonline.org/volume/1604-1629/survey/parliament-1604-1610) after 1604 frantically looking for opportunities to increase their representation because the parliament became such a long haul. This issue of parliament party building is dealt with by “The Earl of Salisbury and the "Court" Party in Parliament, 1604-1610” by David Harris Wilson (1931).

There were two issues that led to this. The first of which was King James' favoured proposition of union between the crowns of England and Scotland as Great Britain (the first serious proposal of this idea). To the relatively (for the time) nationalistic, and mutually xenophobic, populations of England and Scotland this was a potential threat to their identity and laws. It became a great issue what the effects of this union would be and how it was to be done. The underlying uncertainty and xenophobia meant it was never resolved. Judith M. Richards in "The English Accession of James VI: 'National' Identity, Gender and the Personal Monarchy of England" (2002) explains this fundamental cultural anxiety well. The other issue was the systems of wardship and purveyance. Respectively the ability of the Crown to raise fees for the fostering (wardship) of important orphans, and the right to gather supplies (purveyance) for the Royal Household at below typical prices. In the increasingly commonwealth-y political climate of the time, with a great deal of concern in general about financial difficulties, these old rules of budgetary convenience to the Crown came under scrutiny. Over the course of the sessions to come negotiations would ensue over how to reform these but at the time of 1605 the main concern was that the Commons had been more stubborn on raising that debate than expected. Pauline Croft's "Wardship in the Parliament of 1604" (1983) and Eric Lindquist's "The Failure of the Great Contract" (1985) explain the longer running issues of negotiation that occurred in the Blessed Parliament for those interested.

It was into this situation that the legendary moment of Guy Fawkes caught in the undercroft with the barrels of gunpowder entered. In a time of extreme religious tension where the Protestant mainstream was constantly afraid of popish plots, this was just the distraction needed to unite the Commons, who saw themselves as loyal subjects after all, behind the King and the Protestant Settlement given the alternative they had just been reminded of. When the King wanted it celebrated the parliament positively jumped to demonstrate their filial loyalty. It must be noted that one of the main sponsors of the Act to mandate the new celebration, Edward Montagu, had just recently been reduced in his local offices because he had joined in a Puritan-sympathetic petition that had upset the King (the deprivation is mentioned in his Dictionary of National Biography entry). It was the perfect opportunity to prove himself by uniting around their common enemy. The text of the Observance of 5th November Act is available in Eyre and Strahan "The Statutes at Large, of England and of Great-Britain: From Magna Carta to the Union of the Kingdoms of Great Britain and Ireland. 1708-1726" (1811)