What kind of nest is this?
This is the chrysalis stage of the monarch butterfly, confirmed with one of our UK Extension Entomologists. He says it should emerge in 7 - 10 days. Is it possible to leave the chrysalis hanging there until the butterfly emerges? That would be the best case scenario.
If it must be moved, detach it carefully, keeping the stem intact. Then carefully tie some light twine to the tip of the stem and suspend it in a landscape shrub. With the way the butterfly will emerge, the chrysalis needs to stay in a hanging state.