The problem with simply turning the british monarchy into an autocracy is that even before 1795 it had essentialy been turned into a parlimentry monarchy. The revoloution of 1688 had set the precedent for parlimentry supremacy over the monarch and royal involvement with poltics in the 18th century was patchy amd unstable. Neither George I or II spoke english and took a very limited position in government ,and even George IIIs role was limited as he aged. by 1795 the heir apparent was running things ,and the prince regent was far more concerned with his addiction to hedonism
Instead , i would prefer to put forward a far more radical thesis. Towards the end of the 19th century Immigration reached its peak ,producing very visable minority groups in London and the Major cities ,and a spate of Anarchist/ Anti Semitic violence. In OTL this was very short term and never amounted to much , but TTL is different.
As the century draws to a close previously factioned anti-immigration parties begin to merge under a young charismatic leader , Captain Haig. After becoming head of the Imperial Party(IP) in 1888 ,Haig makes rapid political gains by playing off the Irish Question and fenian attacks ,calling Gladstones attempts to pacify the country as "Selling out the Empire to the Barbarians". The final straw was an Anarchist assasination attempt on the queen in 1896. Although the queen was uninjured , Haig successfully uses the event to pass the Defence of the Relm Act (1897)(DORA) ,providing for sweeping powers to round up "Undesirables" ,Censor the press and curtail public meetings. Haigs new political power and the raising image of the IP secures him the position of Home Secretary ,in charge of the Police and the new "Special Constabulary"(SC) whose job it is to police radical political elements.
By the spring of 1899 the IP is facing challenges to the DORA in Parliament. Facing increasing domestic pressure ,Haig uses IP elements within the army and the paramilitary SC to stage a coup on Mar 15 1899,forcing the queen to make him prime minister and suspending parliament ,using elements of DORA to maintain Britain as a police State.