The English monarchy did not begin with Alfred of Wessex. He contributed to the unification of Anglo-Saxon lands to a place that can nebulously be called "England", but there's several issues in tracing the monarchy all the way back to him. Firstly, he wasn't the first king from the House of Wessex, and I can see no reason to discount anybody prior to him other than because Alfred was considered a glorious king and there's some precedent in arbitrarily beginning lists with likeable people. Secondly, the Anglo-Saxon monarchy was indisputably annihilated in AD 1066 during the Norman invasion, and the dynasty of kings beginning with William can in no way be considered part of the same monarchy. Thirdly, in addition to Cromwell, the preexisting English monarchy was basically eliminated during the Revolution of 1688, since William of Orange wasn't the legitimate throne-holder; James II was.