With a velomobile, in the UK, I strongly suspect you'll be tied to using the roads. Many bike paths have width restrictions or tight chicanes; I even have to walk the tandem through some. Transitions between bike paths and the road are often where you get barriers to stop motorbikes. They'll probably stop you. Many stop wheelchairs despite that being illegal.
There are a few places I can think of where a velomobile would be particularly tricky, like ferries where bikes are treated as pedestrians' luggage.
I've only ridden in that area for a few hours, and not on routes that would help you, but the impression I got from National Cycle Route 72 was not favourable for a Velomobile.
You'll be starting at North Shields if you're getting off the ferry, and a logical route from there south uses National Cycle Route 1 (EuroVelo 12) much of the way.
Let's put your start and end points into a routing engine:
- RideWithGPS is popular, but only has one mode for cycling, and indicates a lot of unpaved surfaces - they might be all right, but they might not, routes using the Shields Ferry.
- Komoot isn't perfect but it's my preferred option for a couple of reasons: It's more informative, and it has several cycling modes including "road cycling". This sticks to paved surfaces (or at least warns about unpaved ones), and is less likely to use bike paths than "bike touring" mode.
- Google isn't even worth linking to - it's bike routing is very poor indeed.
- Cyclestreets gets an honourable mention but isn't customisable enough to work here. Their Quietest route won't be any good for you, their Fastest and Balanced are worth looking at for inspiration.
Carrying on with Komoot, you get some warnings and information:
- A ferry after 2.14 km - that's the one RwGPS uses as well.
- Unsuitable surface after 46km - this is only short and might not even be true.
- Steps after 2.13km. That's to get to the ferry. The ferry is however supposed to be wheelchair accessible, so there might be a ramp, which you might be allowed to use. At this point I'd look for a bridge (upstream, only a short detour).
Looking at its Waytypes and Surfaces data there's more useful information:
Street, Road, and State Road should all be fine, though the traffic might not be great. Cycleway, Path, and Access Road would make me suspicious. The Singletrack is probably an error, but if real, it's likely to be narrow as well as unpaved.
At this point I would just tweak the route by dragging to avoid all of these sections, which are shown graphically under the elevation data. Even in Road Cycling mode Komoot will try quite hard to avoid main roads (A and to some extent B roads) and may need to be dragged back on track.
You might want to look further into the cycle infrastructure, if the roads look nasty. You've got 2 options:
- Where the route meets roads, Google Streetview is really useful. This crossing, on a realistic route, looks workable if not ideal. Street View is also of some use for checking what roads are like, but they've often been imaged at fairly quiet times.
- Away from roads, I'd go to OpenStreetMap's cycling view. Cycleways are shown as solid blue; on-road bike lanes are dashed blue and probably desirable for you.
The "Query features" tool (mouse pointer icon with a question mark) allows you to click and find out more about what's mapped. I clicked on the road crossing I've linked to in Street View, and one of the nodes has "barrier=bollard" - which you might or might not get through on that sharp bend (but it looked passable on Street View).
There's even more detail in OSM, which you can explore with a (free, fairly anonymous) editor account. That's where you might find widths of barrier nodes.
Links to route planners are very rough routes for your trip, just for illustrative purposes - take them and customise them by all means, but don't ride them without checking for yourself.