The Anglo-Saxons (who arrived in the 5th century) fortified their villages with stockades, but this was to keep out wild animals as much as neighbours. They were nowhere near as organised as the Romans and so they did not build anything substantial.
However, when the Vikings arrived there were many struggles for land between Saxons and Vikings. Without fortified places, battles moved quickly across the land. Eventually, Saxon King Alfred decided to build walls around many of his towns and make them easier to defend. He called them burhs.