This was long after the Brits had happily deposed a king and made the country a sort of republican democracy, although they'd reverted to kingship not long after. Thomas Paine was just being born and he was a strident advocate of republicanism via writings like 'Common Sense'.
I dont know you'll find any direct evidence of what 'most' people thought on the matter as I doubt that that evidence has been collated. However I believe that few would have thought the King was divinely chosen as such. The Brits were well under way in their slow emasculation of the royal authority by Parliament and its hard to image that would be accepted if most of them believed he had been placed there by God. Indeed The Glorious Revolution made no reference to Divine Right, whereas the previous Catholic Kings had attempted to claim it a number of times, thus implying it was no longer regarded as relevant. It was largely a claim made by Catholic monarchs and not by Protestant ones of the era, so it had become linked to the now defeated Catholic movement.
The nature of the methods they chose around then to pick whatever Kings they wanted, excluding the catholic ones, roping in distant relatives, would suggest a strong practical streak in their attitude to royalty. Little regard given to what God would want, most regard given to what suited the publics mind, a nice Protestant king with not too many grandiose ideas of total power.
I think you'd find the (largely closet) Catholics still believing in some degree of Divine Right, and few of the Protestants. There was also a growing republican sentiment which of course believed in no kings at all.
No. 300 years ago would be 1714. Within a lifetime of that date, Englishmen had (a) executed one Stuart king (1649), (b) deposed another (1688), and (c) instituted the Act of Union (1707). There were some attempts to revive the popular culture of royal providence following the so-called "Popish Plot" against Charles II, but the divine ordination of the House of Stuart certainly fell on harder times during the Glorious Revolution. Furthermore, this period birthed modern party politics. The Jacobite faction supported the return of the Stuarts over the Hanoverian succession in the next year (1715), and they treated it as a civil, not a religious, concern (eg, the King as a counterbalance to Parliament).