The IVA requirement is an interesting one. It is absolutely correct that if you want to build a new trailer today, you need to get an IVA test done on it before you can legally put it on the road. The requirements aren't difficult. The Inspection manual is available here:
How trailers are inspected when they're being approved under the Individual Vehicle Approval (IVA) scheme to make sure they're safe to be used.
www.gov.uk
Domestic trailers tend to be category O1 (up to 750kg laden) or O2 (up to 3.5 tonnes laden).
However, the really silly thing in the UK is that there is no legal requirement for a trailer to be registered, so if you get pulled, there is no reliable way of knowing how old it is! I suspect there are lots of relatively new trailers around, which, as far as "Plod" is told, are actually old trailers that pre-date the requirement to have an approval test, but that someone has "restored"...
Leaving that aside, I've built plenty of trailers in the past. If it were me, I would:
1. Decide what maximum weight you want to tow and what size / type of objects. Do you want a car trailer? Box trailer? Boat trailer? Horsebox?
2. Check your towing vehicle and its maximum capacity. Most cars can tow up to a 500kg unbraked trailer. Some larger ones and vans, can tow up to 750kg unbraked.
Once you know this, you can select some suitable suspension, brakes, wheels and tyres and a towing hitch. Pretty much any trailer over 750kg laden, will need brakes, which bumps up the cost and complexity.
3. The design of the suspension will dictate your chassis material. It's not impossible to build one out of wood, but with something like an Indespension unit, the mounting points cover a very small footprint and I imagine it will be quite hard to safely feed the loads from that, into a wooden structure. Personally, I would go for steel, every time! However, I'm comfortable with welding. You don't HAVE to use Indespension (or one of the many copies of Indespension) available - I built my dad a trailer that used a salvaged Reliant axle and leaf springs, but Indespension-type units are very widely available.
4. Maybe look on some trailer parts websites to see what's available - places like Towsure, Trailer Tek, Autow Warehouse... there are dozens out there, where you can buy pretty much everything you need. Some places will sell you a complete, flat-packed trailer kit!
Explore flatbed and box trailers designed for UK roads. Easily transport luggage, equipment, or garden waste with reliable tow bar compatibility at Halfords.
www.halfords.com
Maybe post back with what type, size and weight you're thinking of, and we could take the next step.