I tried this when I had a similar problem years ago. Switch the fridge off and take your time examining it from every angle. It's usually pretty easy to work out how things like door seals and light covers etc come off because they're designed to be replaced (don't attempt to dismantle anything if you're not sure you can put it back). Once you've removed whatever you can, use a sponge to cover everything with Milton sterilising fluid. The interior of a fridge is designed to sustain spillage so you should be able to slop the solution about generously. Such a persistent smell might mean there's a hairline crack somewhere inside the fridge where milk has escaped. If this is the case the Milton solution should chase after it. Most importantly, let the fridge dry out really well before you switch it back on. The smell is caused by bacteria digesting their food and bacteria loves damp dark places.
Incidentally, Milton fluid is also good for cleaning mildew off shower curtains.