Oh my dear me. It was indeed a republic, with democracy as power was primarily invested in the democratically elected Parliament. After Cromwell, in the Restoration it didn’t revert “back to autocracy” but back to a constitutional monarchy with a (still) democratic Parliament.
“Whereas Elizabeth I’s regime was a monarchy with traces of a republic, Cromwell’s regime was a republic with traces of a monarchy. Indeed, in some ways the term might be regarded as more truly applicable to the Interregnum because, unlike Elizabethan England, it actually was a republic.”
www.olivercromwell.org/wordpress/the-monarchical-republic-of-oliver-cromwell-cromwell-day-address-2015/
“The Commonwealth was the political structure during the period from 1649 to 1660 when England and Wales, later along with Ireland and Scotland,[1] were governed as a republic after the end of the Second English Civil War and the trial and execution of Charles I. The republic's existence was declared through "An Act declaring England to be a Commonwealth", adopted by the Rump Parliament on 19 May 1649. Power in the early Commonwealth was vested primarily in the Parliament and a Council of State.”
en.m.wikipedia.org/wiki/Commonwealth_of_England
“In early December 1648, frustrated by the ambiguities and hesitations of those negotiating with the defeated king, a detachment of soldiers purged Parliament of its most conservative MPs, opening the way for the hasty organisation of a High Court of Justice and the consequent trial of Charles I. As the king resisted the legitimacy of the court and refused to enter a plea, power passed to the more radical military and political leaders, as they became increasingly interested in exploring republican solutions to the political crisis. After multiple attempts to have Charles recognise the court by entering a plea, his judges found him guilty of treason. He was beheaded on 30 January 1649 outside Westminster Hall and, four months later, England was formally established as a republic. The English republic was rooted in the religious and political idealism of its visionaries, administrators and apologists.”
”The English republic did not collapse because of external pressures. After all, the revolutionary regime had excelled in its military activities: having conquered Ireland, Scotland and Jamaica, and having quashed the last serious Royalist rebellions, its future might have appeared to be secure. Instead, the republic collapsed in upon itself. It grew increasingly indebted to the military and by the later 1650s the arrears of pay that were owed to soldiers grew so significant as to threaten to bankrupt the regime. Its administrators pursued different political settlements for England, Ireland and Scotland, creating strategic ambiguities as to what a republican government should look like and the extent to which it should draw in at a local level the traditional social leaders. Most seriously, the republic proved to be incapable of sustaining the religious and political ideals upon which it had been founded.”
www.historytoday.com/history-matters/end-english-republic