so stronger, but not absolute, monarchy.
Yes. Most likely a Semi-Absolute Monarchy. Like what Portugal and to a lesser extent Spain became. The Portuguese Crown became financially independent via gold in Brazil, so there was no need to call the Portuguese Cortes. I think that Parliament would only be called when major laws, like an act of union, need to be passed. Besides that, it would remain uncalled and unwanted.
As for the development of World history, well we wouldn't have the Westminster parliamentary system. Though with taxation powers now lying with the Crown, we could see a more active English foreign policy. Also the Church of England would remain very much High Church, with other denominations (ie Presbyterians, Puritans ex,ex) would be repressed and discriminated against. Ironically, British Catholics would probably benefit the most, as the penal laws weren't enforced under the Personal rule of Charles I.
Besides these, I'm not sure. The Colonial Empire would remain similar, though elective assemblies would no doubt be repressed or never created. The East India company would also remain the same. Maybe, if the English turn and defeat the Scottish Presbyterians, we would see an earlier Act of Union. It might even end up being similar to the Spanish Nueva Planta decrees, with Scotland and maybe Ireland simply annexed by decree into a new Imperial Kingdom.