Small bird like a house wren returning to our lounge

Hi there! I wondered if anyone can help. We live in West Yorkshire & for a few weeks, since early November, we have had a tiny brown bird (from looking online it looks like a House Wren) come in to our lounge/kitchen. We have no idea how it gets in but it likes to hide in a large monstera plant we have in the corner or now that has been replaced with the Christmas tree it is hiding in there. It probably comes in once a week but twice this week.
I have a vague memory of this happening a few years ago but definitely don’t think it was as frequent & I’m not sure if it was the same time of year. 
We do have a log burner that I’m wondering if it’s somehow coming through although we keep the door closed I think there are holes in the base for airflow.
It’s totally harmless & very sweet but I don’t know if we could end up with problems nesting down the line (especially if it is coming in through the fire) or if we are away for a few weeks will it be able to leave. Any tips/advice welcome!

Have added pics.