You can make a safe run for rabbits outside, but the temperature difference between outdoors and indoors should preferably not be more than 10 degrees Celcius up or down.
A safe run has netting on all sides, 1/2 inch by 1/2 inch welded netting is the best. The absolute best thing is to dig out an area and put down netting and then fill up with earth, but if you can’t do that, netting on top of grass is fine. Girl buns especially likes to dig and they can dig quite impressive tunnels in a very short time. Predators can also dig in, but most predators are active at night and that won’t be a problem if the buns sleep indoors. There must be a roof on the run because otherwise birds of prey can swoop down on the rabbits and kill them.
Since you are in England, the buns need to be vaccinated against Myxo, RVHD1 and RVHD2.
ETA: Our member Vienna Blue In France lets her buns out during the day. She’s in the north of France (=similar climate as England). You can PM her and ask about her arrangement.