In OTL, the Parliamentarians won the English Civil War. This led to massive upheavals in the government that hadn't been seen before to this degree with the Monarchy being banished from the realm. Afterward, Oliver Cromwell became the Lord Protector, taking on a role much like the monarchy. After Oliver Cromwell died in 1658 his son Richard Cromwell took over as Lord Protector. Richard was unable to retain this position (being known as 'Tumbledown Dick'), which led to the "restoration" of Charles II as King of England and Scotland.
The POD in this scenario is that many influential Parliamentarians such as John Lambert were more republican rather than wishing to keep a monarchy.
Another POD is that Charles Fleetwood, husband of Oliver Cromwell's daughter, actually took over as Lord Protector rather than the inexperienced Richard Cromwell. This led to a Republican England and a different history of European development, colonialism and world alliances.
After Cromwell had won the English Civil War the 'English Council of State' was created from 1649 until 1653. During this time many people who had previously been Royalist or still wanted a monarch-like ruler (such as John Lambert) had their minds changed after Cromwell had given a long speech about a monarchy.
Also when some of them asked Cromwell as to whether he'd like to be the new Monarch he said outright he didn't wish to take on the roles of the monarch. Due to this a new constitution called the 'Instrument of Government' was written, which allowed for a much more Republican England. While Cromwell's post still lasted for the lifetime of the Lord Protector it had less power than in OTL. Though the Lord Protector was still very much like a dictator the parliament still had a say in legislative and government affairs.
Also after Cromwell was weakened due to a kidney stone he realized his son, Richard, was too weak to become the next Lord Protector. He wrote to the parliament saying his heir was to be changed to his son-in-law Charles Fleetwood. As a result of this Charles Fleetwood continued with Cromwell's hard lined attitude and ruled with an iron fist with Scotland and Ireland. The army followed him and admired him, he changed England for the better.