For the last couple of months I have been waking up with an aching lower back every morning. After getting up and moving around for 5 mins it eases off.
It's not sore, but aches, and it happens weather I train or not.
Any ideas why this is happening and how this could be prevented?
Baz
Could be the position you most commonly sleep in as well maybe. If you sleep on your stomach that could cause a fair bit of low back pressure and tension. Also you could try using a body pillow to help keep things in better alignment while you sleep.
Leigh - Have you tried changing your mattress? Might be too soft, might be too hard
Mattress makes a huge difference. If I sleep on one that's too soft my back aches constantly. Hard mattresses are better for me but everyone is different.
I find that doing a little bit of yoga in the morning helps a lot also. It doesn't have to be much - 10 reps of cobra alternated with downward dog works well at loosening everything up. 
Just your lower back? I have aches in my hands and feet in the morning. Waiting for test results to see if its rheumatoid arthritis
^ Speaking of the couch stretch, i was seeing a physio a few weeks ago for an ongoing knee problem, and she told me to stop doing couch stretches (after i demonstrated what they were) as they put too much stress on the knees and might cause problems in the future. First time i've heard of this, anyone else heard similar?
martinburke - As in a physical therapist?
I'm going to withhold my immediate thoughts because I try not to generalize about an entire occupation just because of my personal and professional experience.
But I'm wondering how that stretch could possibly stress the knee.
Yes, physical therapist. She didn't elaborate on what it would do, but she did give me an alternative stretch. Basically kneeling on a towel with one knee, other leg forward in a lunge position, and then push my hips forward to stretch the hip flexors. Ironically this stretch felt like it was pushing my knee cap up my thigh and putting it in a precarious position, and after a few days i began to develop knee aches so scrapped it.
BazUK - For the last couple of months I have been waking up with an aching lower back every morning. After getting up and moving around for 5 mins it eases off.
It's not sore, but aches, and it happens weather I train or not.
Any ideas why this is happening and how this could be prevented?
Baz
You could give topical magnesium a try for a couple months if you wanted:
http://www.ancient-minerals.com/products/magnesium-oil/
It's a bitch getting oiled up and stay so for 20 minutes everyday but it could do the trick in your case if you're deficient.
I have the same issue. I started foam rolling a lot and can feel it right to the left of my spine in my lower back. I try to stretch as much as I can especially before I play hockey or I feel miserable afterward. 
I had the same problem. I use a foam roller and a lacrosse ball every morning now for about 5 min and the pain is now gone totally . I focus the ball on lower back one day then hips/upper glutes the next. The ball sucks but if u search out tight /sore spots u will get used to it.