Suggestion from Robert Whittaker @rjw62 via email:
I've found a useful leaflet plugin that I use on my tools: https://github.com/osmlab/leaflet-edit-osm that adds an "edit" button to the slippy maps. See e.g. https://osm.mathmos.net/postoffice/branch/97573 . I did hack the leaflet-edit-osm.js file slightly though to remove the &editor=id part so that it will use the mapper's default editor rather than forcing iD.
Suggestion from Robert Whittaker @rjw62 via email: