No signed cycle route on A27 eastbound west of Fareham

Cycling on the A27 eastbound west of Fareham, at the Titchfield Mill junction there are no signs to indicate the way forward. The (shared?) footway route over the Meon bridge and onwards is in fair condition and avoids the fast traffic, but I saw not a single cycle sign or symbol until the edge of Fareham, where an absurdly short footway section is marked. I believe this section of the A27 was upgraded quite recently. I still do not know if I was breaking the law for all or part of my journey today.