Bunny runs can be fine as long as they are secure (no flimsy walls that they can push through or squeeze under) with some sort of overhead protection as well, and best of all, supervision. An ex-pen with some kind of covering (a sheet?) could be a good temporary run structure as long as people are around to keep an eye out for anything that might happen.

I think it’s fine if the run is constructed well and there’s no way for the rabbit to escape or a predator to get in.

I don’t let my bunnies out because we have a crazy tick problem and I don’t want them picking some up in the yard.

I agree with the covered run because it’s the predators overhead that can swoop down in the blink of an eye.
Another factor to be cautious about is pesticides on the garden. If you are far from neighbors with airborne chemical sprays and do not use your own, then it’s much safer. But in a well groomed neighborhood, there’s a risk of lawn and tree sprays being in your garden where bunny may eat.
I like the xpen suggestion, but by all means build something if you are handy and creative. Then show us pix.

I built an outdoors run for my rabbit last year, but he didn’t spend much time there because most days last summer were rainy. The netting must be weld mesh, not just ordinary chicken-netting because small predators like weasels and ferrets can easily bite through chicken-netting. And your bunny need to have shots against myxie and RHD since both diseases are common in England and very deadly, but I guess you know that.

I don’t have a picture of the run but it has netting on all sides, top and bottom as well so predators won’t get in and the rabbit won’t dig himself out.