It was certainly the law at that time in England & Wales. Although the development over time was rather roundabout.
Up until 1753, as long as a marriage was conducted by an ordained clergyman of the Church of England in England or Wales then that was all that was needed. Although, as I understand it (I may be wrong), prior to that, there was a common law rule that people only gained their majority when they were 21.
In 1753 the Clandestine Marriages Act was passed and it came into effect the following year. This basically said that anyone under the age of 21 needed their parents permission to marry by licence or for banns to be read.
This came up on a recent thread here:
https://www.mumsnet.com/talk/genealogy/5381881-british-military-question-and-g-granddad-mystery
Although this did not apply to Scotland and Jews and Quakers were also exempt. Non-conformists and Catholics were required to get married in Anglican churches up until 1836.
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However, you're talking about Belfast, and things were different with Ireland.
Having said that though, there was the Marriages (Ireland) Act 1844. This said that for any non-Catholics under the age of 21, they needed the permission of their parents in order to marry. However, if the parents did not consent then the person could make an application to the Lord Chancellor or to the Master of the Rolls for consent instead.
As I understand things (I may well be wrong), for Catholics there was no requirement for parental consent.
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"...as the bride's male relatives were all diehard Orangemen"
In that case it would appear that the bride would have required her parents consent at this time.
As others have mentioned I have seen several cases of young women who have claimed to be 21 at the time of their wedding but their birth certificate definitely says that they were younger.