Welcome to OpenStreetMap and thanks for adding this.

If you're adding a footpath as a highway=footway, you often don't need to add any access tags, as the default access in the UK is assumed to be foot=yes (only).

Adding access=no won't affect pedestrian routing, but will cause the path to be rendered by OSM Carto (the default map style) as a faint grey dotted line rather than the usual red.

The iD editor isn't that helpful here, as it presents general access and motor vehicle access for all highways, even ones where they are unlikely to be appropriate (e.g. footway, cycleway, bridleway, pedestrian and path).

https://wiki.openstreetmap.org/wiki/OSM_tags_for_routing/Access_restrictions#United_Kingdom