Hi Rose, sorry I cant help much with which came first, wattle and daub or cob. But, wattle and daub was very prevalent during the Tudor period. The houses were oak frame structures, and the wattle was then used to fill the spaces between the frames. Then the daub was added to stop wind whisteling through. The daub was then "painted" with a limewash to help waterproofing. Only the very rich had ornate woodwork, just to prove how rich they were. I think the poorer people used the cob build,because of the strength and cheapness of it. Lets face it, it was free. Just dig up some mud, get some old straw from the fields, and add water. Mix well, and dry out.
Because most houses were built in the wood frame style for hundreds of years, and the fires were on a hearth in the middle of the living area, the whole house was warmed. But after the great fire of London, a law was passed saying that, all houses were rquired to have a stone chimney and hearth. This was to cut down the risk of a repeat of the fire.
Later, when baked mud bricks had been (invented), the wattle and daub was replaced by bricks. A lot of old Tudor houses now have these brick fills in intricate patterns. So maybe it was a local thing, cob more in the country, and wood frame and wattle and daub in the towns and the lords manor.
May not be entirely correct, but not far off. Hope this helps.
Peter.