The country had had a spell as a republic not long before, and had not enjoyed the experience one bit, gratefully welcoming the rightful King back following the death of the dictator Cromwell. I doubt that the experiment would have been repeated so soon. The death of Queen Anne is an at least vaguely plausible POD for a temporary or perhaps permanent split between England and Scotland, but both would have remained monarchies for the time being, I would think.
As they have ever since, as well as united. I think the greatest peril myself was in the immediate aftermath of WWI, or perhaps a few years later with the General Strike turning into outright revolution. Queen Victoria's very long reign inevitably contained periods of unpopularity for her personally, but only a very small minority were opposed to the Crown continuing. I haven't gone into it deeply, but offhand I don't think there's a realistic POD earlier than the ones I mentioned.