I have prepared a basemap in Mapbox which includes imported data (basically, marker points). I was expecting these markers to show when using that project as a basemap in CartoDB, but it only shows the basic tiles. Is anyone aware of this issue or how I could go about including the markers from Mapbox in CartoDB?
When using a Mapbox basemap in CartoDB, tiles are all you're bringing in. CartoDB has no concept of the underlying data you used to build your basemap, it only knows how to access the tiles, which are pictures made using that data.
It sounds like you want to use CartoDB's wizards to style your points and add interactivity to the map. The only way to do this is to load the marker data into your CartoDB account.
Another option is to use leaflet (via cartodb.js or mapbox.js) to render and style the markers client-side.
Can you post a screenshot?