Technically, you just need to clear the body by millimeters on normal road conditions. Deflated tyres only broaden at the base.
But in off road conditions, you will experience the trailer slipping sideways into a rut. In severe circumstances, you will exceed the static load that is normally carried on both wheels, being exerted sideways on one wheel only. (This is due to the trailer falling into the hole and the deceleration of the trailer as it lands in the hole, adds G's to the static load, so a 3000lb load normally carried on two wheels can land up being 3500lbs or more, being exerted sideways on one wheel only.)
This will push the leafsprings sideways and depending on the tolerance and flex you have between all joined parts (shackles, poly bush, link plates) will determine the sideways movement of the axle.
Our build on the Metalian trailer has half an inch gap. Our shock is mounted vertically in the wheel arch between the wheel and the trailer body. We don't see tyre marks on the shocks from trailers that come in for repairs and servicing, so our experience is that half an inch will suffice.