I take it you are talking about the wall, rather than the
Hadrian's Cycleway (NCN 72)? Funny name, come to think of it, did the Roman's have bikes

? Also slightly surprising that the route follows so much of the Cumbrian coast before getting to what I always thought was H's Wall cutting across East/West. I'd love to take the bike south and explore ...
Oops, back on topic - I really enjoyed the Coasts & Castles route, although with hindsight, in places I would probably divert off the signposted route, as some of the surfaces are really quite rough and hard work for loaded bikes. But some of the rough bits are well worth the effort for the amazing views, in my opinion anyway. It's a very easy route to get to and from by train along the East Coast main line, so you can split it in into "weekend-sized" sections.
T