As was stated Ernst Augustus war an unpopular figure. I don't know enough British History to know if he would be overthrown though I believe that's not so sure: there were always some discontent with House Hannover from what I understood and yet no monarch of that dynasty was overthrown. Even George IV, who was unpopular, stayed on the throne even if his reign only lasted 10 years: he had bit Prince Regent in the late years of his father George III though, meaning he was in charge of power longer than that.
It will probably depend on his attitude as King of both Hannover and Britain and on how he rules: unless he pisses off too many people, he has chance of staying on the throne. There were many monarchs who held on their throne despite their unpopularity be they British or not.
On a side note, the list of Kings of Great Britain & Hannover will probably be altered. First, there is the question of Ernest Augustus' regnal name: would he go for Ernest Augustus like OTL, chose simply Ernest I or Augustus I or even chose another regnal name because of his accession to the British throne?
Second, butterflies of No Victoria gets rid of her children and, as such, affects several European dynasties and not just Britain/Hannover: for example, there will be no OTL Wilhelm II of Prussia as Victoria was his grandmother. As a result, the British bloodline of Ernest Augustus will be affected: George V is probably kept and maybe even Ernest Augustus II (his parents married in 1843 and butterflies might not be strong enough to change its course) but after him that's a no. Why? Because being King of Great Britain is a lot more prestigious than King of Hannover: so you can eventually expect a better wedding for Ernest Augustus II. And even if George V loses Hannover like OTL, his dynasty will remain a regnant one: regnant royals had more presitigious marriage than non-regnant ones, so this will probably affect Ernest Augustus II's bride.
Third, we have to take into account "unexpected" event: an ATL WWI is still possible and if it pills Britain against Germany, it might have the effect of having the British monarchs giving up germanic names like Ernest sounds. Remember that, in OTL, the British Wettins became the Windsors because of WWI.
I once launched a "What If" thread with this POD.
https://www.alternatehistory.com/Discussion/showthread.php?t=194984
Having Charlotte rule instead of Victoria does interest me, although I don't know British History enough to answer the question.
On a side note: if Charlotte were to survive childbirth in 1817, then there are chances her baby would, be it a boy or a girl. So, dynasty is probably assured if said baby doesn't die young and/or Charlotte's ability to procreate isn't affected by her pregnancy (difficult pregnancies could rendered women sterile).