It is... and it isn't.

Elizabeth II is a descendant of Alfred the Great of Wessex. Alfred's a pretty good point for first English monarch. But you can't go straight down and say she's a direct primogeniture descendant of the previous kings. There's a lot of breaks where the crown went to a distant cousin.

For example William I was Edward the Confessor's first cousin once removed and via a female line at that. Plus he wasn't a descendant of Alfred. It'd be four more kings before the Wessex and Norman families combined, and we got a direct descendant of Alfred back on the throne, Henry II. Henry II was Stephen's second cousin once removed, and Stephen was Henry I's nephew. Edward IV and Henry VI were third cousins, meaning they only had a great-grandfather in common. When Elisabeth I died the crown went to James I, her second cousin twice removed.

There was even a period where England didn't have a king, although his descendants reaquired the crown. But again when William & Mary died, it went to their second cousin George I. And I do mean their cousin. William & Mary were first cousins, so George was a second cousin to each of them.

In one way or another a descendant of Alfred has almost always sat on the throne. But they've occasionally had to go to some pretty distant cousins to keep it in the family, so to speak. It hasn't consistently gone from father to son (or daughter). Instead it tended to go father -> son -> nephew -> cousin -> brother -> son. The crown tends to wiggle its way through the family tree rather than follow a straight branch directly.