The new bit of the A14 was designed as a smart motorway*. However, I seem to remember reading something about there not being enough parliamentary time available to deal with the legislation required to make it a motorway. So they simply didn't - hence we're stuck with it being an A road. (Though of course it's possible that this was a convenient excuse to avoid using the word "motorway", which for some reason terrifies anyone at National Highways.)
The Lower Thames Crossing is a far more stupid example of "not a motorway-ism": a high capacity road, linking two motorways, designed to take long distance and international traffic, which will have traffic class restrictions on it from the day it opens. Sounds like it should be a motorway, right? Wrong! It's being designed as an A road...
*As usual, I should mention that "motorway" is merely a legal distinction from other roads; it is completely separate from the standard of the road (eg: number of lanes). The fact that, conventionally, motorways is Britain have had a hard shoulder and usually 3 lanes each way (but sometimes 2 or 4) is irrelevant. A road with 4 lanes each way and a hard shoulder can be an unclassified road**. A single carriageway road can be a motorway.
**Well, technically not, as I think the design standards decree that a non-motorway road cannot have more than 3 lanes. But that's simply an arbitrary statement and is besides the point...