Contrary to the premise of the question, not all Catholic bishops in the British Isles are Right Reverend. Since the 1860s all Catholic Bishops in Ireland have been Most Reverend. In England, Wales and Scotland Most Reverend is reserved for archbishops and Right Reverend for bishops. This Most/Right distinction is also used in the Church of England and Church of Ireland, except that the Protestant Bishop of Meath and Kildare is a Most Reverend.
The distinction is mirrored in the secular peerage. In the English Order of Precedence, C of E archbishops rank below Princes but above non-Royal Dukes, while bishops are between viscounts and barons. Dukes are Most Noble while Viscounts are Right Honourable; so it is perhaps appropriate that archbishops use the same grammatical intensifier, Most, as dukes, and bishops use the same grammatical intensifier, Right as Viscounts.
Erasmus (1466 - 1536) wrote numerous letters which were collected, numbered and published. In May 1519 he wrote letters to the Most Reverend Archbishop of York (letter 967) and to the Right Reverend Bishop of Durham (letter 974) which shows the distinction was made before the Reformation reached England.
After the Reformation the Irish sees continued as before both in the Church of Ireland and in the Roman Catholic Church. So there were two bishops of Derry, one Protestant and one Catholic; and two Archbishops of Armagh, one Protestant and one Catholic. Though there were gaps, and later amalgamations especially in the C of I. The honorific Most or Right Reverend, pertaining by law to the Protestant clergy, was used also for the Catholic clergy within the Catholic community and often, by courtesy, outside it.
In England the Roman Catholic succession to episcopal sees died out. From 1685 to 1850 England's Catholics were served by Apostolic Vicars of which there were 4; for London, Western, Midland and Northern regions; increased to 8 in 1840. These Apostolic Vicars were in fact bishops, but not of anywhere in England. They held titular sees in Islamic countries which had once had resident bishops, but where there were no longer any bishops, or even any Christians.
In 1850 a new Roman Catholic hierarchy was erected in England. It did not replicate the Church of England: there was no Catholic Archbishop of Canterbury to rival his Protestant counterpart. Instead there was an Archbishop of Westminster and twelve Catholic bishops, all of towns which had no Protestant Bishops; but including Bishop of Liverpool and Bishop of Birmingham, two of England's greatest cities. These had, as yet, no Protestant bishops, as they were part of dioceses centred on the ancient, but now much smaller, cities of Chester and Worcester.
This had not been expected to be particularly controversial, but it was. Politicians and Protestant Churchmen, Anglicans, right across the spectrum, and Dissenters alike, were outraged and vehemently denounced the Papal Aggression as it was called. Parliament passed emergency laws forbidding the use of such titles anywhere in the UK (including Ireland where they had been used for centuries). There were widespread riots and attacks on Catholic property. Effigies of Cardinal Wiseman and Pius IX joined those of Guy Fawkes and Paul V on Bonfire Night. Even Queen Victoria demanded angrily to know "Am I Queen of England, or am I not?"
The Ecclesiastical Titles Act was largely ineffectual. It was studiously complied with by the English Catholic bishops who never referred to themselves by the titles but allowed everyone else in the Catholic community to do so. In Ireland it was flouted but no prosecution was ever brought. It was repealed in 1871 the same year the Church of Ireland was disestablished.
The campaign to disestablish the Church of Ireland had been led by Archbishop (from 1866 Cardinal) Paul Cullen. It is almost impossible to overstate his influence on Ireland and Irish Catholicism worldwide. He held strong ultramontanist views and sought to bring the Catholic Church in Ireland into line in every way possible with the practice in Rome.
In Italy bishops and archbishops alike were referred to by the superlative form of reverend. So Cardinal Cullen introduced the same practice in Ireland, calling bishops and archbishops alike Most Reverend. A more cynical explanation is that he was quite happy with the distinction between bishop and archbishop when he himself, as archbishop, was a Most Reverend, abolishing it only when he became, as Ireland's first Cardinal, an Eminence.
Since the late 1860s, the practice has differed between Great Britain and Ireland. In most other English-speaking countries, including the United States, the distinction between Most and Right was maintained at least until the early nineteen-thirties.
As described in Andrew Leach's answer, and translated by Matt Gutling, in December 1930 the Vatican decreed that all bishops and archbishops receive the title Excellentiae Reverendissimae meaning Most Reverend Excellency. Bishops and Archbishops were already, in Latin, the superlative form of Reverend and while Reverendissimae is best translated Most Reverend, it could also be translated by other intensifiers such as Too Reverend, Frightfully Reverend, Enormously Reverend etc. The purpose of the decree was primarily about giving all bishops and archbishops the title Excellency, the Most Reverend bit was merely what had long been the case in Latin and many continental languages.
It was adopted in the United States fairly quickly and gradually in some other countries. The Excellency style, the main point of the decree, could not legally be adopted in the UK as only certain categories of persons were entitled to it, as officially determined, ultimately by the King, and not by the Pope.
Since the "Papal Aggression" of 1850 the Catholic hierarchy in England had been anxious to avoid any unnecessary provocation. It is possible they could have called themselves Most Reverend Excellency but there was little point. Even if the Protestant reaction of 1850-51 was unlikely to be repeated on the same scale, still there were multiple undercurrents in the early thirties suggesting caution.
The regaining of the Papal temporalities, as the Vatican State, in 1929 by the Lateran Agreement between the Pope and Mussolini made the Papacy, once again, a foreign power; making it even less desirable that it confer titles on Englishmen. Then there was the situation in Ireland with preparations in hand for the Dublin Eucharistic Congress. The Virgin Mary was being described as Queen of Ireland; although King George V's wife, also called Mary, was Queen of Great Britain and Ireland. The Eucharistic Congress was itself a great demonstration of Catholicism triumphant. Meanwhile the Church of England bishops were themselves distrusted and seen as arrogant and presumptuous, following the Prayer Book Controversy of 1928. (The Bishops had proposed amendments to the Prayer Book, Parliament had rejected them, and some bishops had threatened to turn a blind eye if vicars used them anyway.) There had also been sectarian riots in Liverpool in 1930. Any attempt by Catholic bishops to claim grander titles would certainly be controversial, and might have had unpredictable consequences.
Apart from that, many non-Catholics were coming to feel, and increasingly have come to feel, that Catholic bishops deserve, as a matter of courtesy, to be given parity of esteem with the official Church of England ones. If a Protestant bishop was Right Reverend, why not a Catholic? Any idea that Catholic bishops might be addressed with a higher respect than that given to Protestant bishops could hardly be expected to catch on outside the Catholic community.
In these days of bishops often being called by their Christian names it seems unlikely there will be any change in the near future.