I'm new to QGIS and not really sure what I'm doing; I have a polyline of the UK coastline and I want to add another line 30 km offshore.
Is this possible?
Surely possible. I presume, UK coastline is a closed linestring, or consists of n closed linestrings or multilinestrings as well. If so I recommend to convert it to polygons (or to one multipolygon, if preferred) using Polygonize tool from the processing toolbox, and then apply a 30 km buffer to the resulting (multi)polygon(s) (processing toolbox: fixed distance buffer).
Hint: If the coastline does not consist of closed linestrings, you should first edit your coastline in order to make sure, that it does.
The processing toolbox can be accessed under menu Processing > Toolbox, or Ctrl-Alt-T.