Had something similar years back in my old flat in Cardiff. Cabinets, drawers, the lot. Drove me mental for about three weeks then just stopped.
Honest take though - before jumping to poltergeist I'd rule out the boring stuff first. Temperature changes overnight can do weird things to wooden cabinets, especially older ones. Swansea gets enough damp that the wood swells and releases at night when the heating drops off.
That said, 3am is suspiciously on the nose isn't it. Classic witching hour stuff and I've seen enough over the years to not completely dismiss it either.
What's the rest of the house like? Any other activity or is it strictly the kitchen? And how long has this been going on? Poltergeist activity tends to escalate if thats what it is, so worth keeping a log of dates and times. Seriously, write it down, you'll thank yourself later if you need to build a case for what's happening.