Doing a small dip into the search results for these trikes, it seems there were a lot of them made, primarily for the UK market. That being the case, it's possible the easiest path to getting to an answer is to find someone that "just knows" if the rim conforms to a standard bead seat diameter (BSD) for pneumatic tires. Sometimes details like this don't quite make it on to the internet even if they were known in certain places and times.
If you had to figure it out from scratch, the first thing you need to resolve is what the bead seat diameter of the rims are, or what you'd be asking them to be by putting a pneumatic tire on. The bead seat is the part of the rim where the bead will sit when the tire is inflated. The bead is the steel wire in the tire along both sides.
Measuring the bead seat diameter exactly is a little tricky. It appears in the pictures these rims do have a hook of some kind. What I would do is use the depth gauge on a vernier caliper to take the dimension from the edge of the rim down to where the hook ends, and then add 2mm. The 2mm is about half the thickness of the bead. Call the resulting dimension X. Then measure the outer diameter of the wheel (one way is push the wheel against a wall, put a large box on the other side remove the wheel and then measure from the wall to the box) and subtract 2X. That dimension should be pretty close to the bead seat if there is one.
Once you have that number, you can compare it to one of the comprehensive lists of wheel sizes that are out there and see if it matches anything. The next practical step would be order the tires and try mounting them.
Putting new rims on the existing hubs is another way you could go. You would need to figure out which 16" size will play nice with the fender clearance and then get 3 of them drilled in 20h, but that's all pretty doable.