Some ideas, a few questions. I hope the container you've transferred it to has open drainage holes at the bottom, and that you don't leave it standing in any outer tray which has water in it all the time. It's also not clear whether you had this tree indoors during the Christmas period, and then moved it straight outside once the festivities were over.
Picea does not like soil which dries out all the time, preferring moist but well drained conditions. If you left yours in a container without drainage holes, or the drainage holes were blocked, no plant likes to be in wet soil which cannot drain because it becomes toxic to the plant. They prefer neutral to acid soil conditions. If you did not water it in well when you potted it on, do so now, allowing excess to drain freely. Ongoing, water when you can feel the top of the compost is slightly dry to the touch, and water copiously, always allowing it to drain freely.
Check the plant closely, looking for striped banding on the needles, any patchy white areas, or fungal pustules or even evidence of insects. If you find nothing, then likely the needle drop, whilst possibly being slightly more than normal, is primarily regular leaf loss, which does occur even with evergreens. I reiterate, keep it well watered, but make sure excess drains away out the bottom - other than that, there's not much you can do. As you're in the UK, there are fewer diseases/infestations here that can affect your tree, so, without further evidence, its likely the problem its displaying is/was cultural.
As the weather is set to warm up significantly again by the end of the week, its sensible to keep it out of hot sun until it has fully recovered. You will find that all yellowing needles will eventually turn brown and drop off; the time to worry is if the yellowing continues and spreads after a couple of weeks.
UPDATED ANSWER: Sounds like you might have green spruce aphid or similar on the tree then, in which case, its worth spraying, as its a small tree, although there's not much point in doing it now, they're active over winter up to end of March. You'll need to get Westland Resolva Bug Killer or Bug Clear Ultra - best time to spray is late August/early September, and again in winter if necessary. Spray thoroughly to run off, trying to get the spray on all parts. In the meantime, give it a general purpose feed in 3 weeks or so (assuming the potting compost you used was fresh and new), and keep it well watered, treat it as if its in intensive care and you need to nurse it!
