I checked the Pogues homepage and it's given as 'gingerlady by my bed'. I'd put my money on it meaning a bottle of whiskey, as he is singing about loneliness and lost love.

Sometimes I wake up in the morning
The gingerlady by my bed
Covered in a cloak of silence
I hear you in my head
I'm not singing for the future
I'm not dreaming of the past
I'm not talking of the fist time
I never think about the last

The final verse is ironic, considering the question:

Now the song is nearly over
We may never find out what it means
Still there's a light I hold before me
You're the measure of my dreams
The measure of my dreams