After the Romans and before the Normans, was cavalry used in Britain?

You often hear that the Saxons would have stood a much better chance in 1066 if they had organised cavalry, but I don't know if they did or they didn't. I'm curious.

What I'm most interested in is the period following the Roman withdrawal and the wars between the Britons and Anglo-Saxon settlers/invaders. Cavalry, as far as I know, was an important part of Roman military strategy, but all you hear from British/Saxon encounters is shield walls and spears.

Did either side use cavalry in any meaningful way or did they just stop using it almost entirely?