Cycling UK, formerly known as the CTC recently put together the King Alfred's Way route. This doesn't involve a lot of new signs marking the trail, but a webpage and map showing the way. It takes in the already popular Ridgeway and South Downs Way routes and links them up with smaller, local routes and some mostly quiet roads.
As you can see from our photos, we had a lot of rain on one day, so decided to stay in pubs and hotels all of whom were helpful with bike storage, though we did ask in advance.
I said to Nick "we might be able to ride through it". He tried. Far too deep and he fell off soaking him and his luggage. Would've been fair enough if he'd yelled at me, but I think he said "Yeah, that's not ideal". I think this is why he fits in so well in Britain.