Is the D3200 still a good camera?

I'm looking for a beginner's DSLR for around £300 and I'm interested in the Nikon D3200. Even though it's a couple of years would it be suitable? Are there any better alternatives? I want to get into photography.

Absolutely. Even if you buy the D750 which just came out, eventually it'll get replaced. And when that happens, does it mean that the D750 stops being capable of being used to make great photographs? Obviously not.
You're just learning, it makes sense to start with a camera like the D3200. Just realize that you're learning know and it doesn't make any sense to buy an more advanced or more expensive camera while you're learning the basics. After a few years when you have a much better understanding on what you need out of a camera, then it'll be time to upgrade to something better suits your needs. Or you just might discover that the D3200 is fine and keep using it.

STILL a good camera? How could a camera model become "bad"? Your question makes no sense.

There's no such thing as a beginner's dSLR. All dSLRs are basically the same, all brands, all models, new and old. You can use any dSLR to shoot anything. If you can still find a Pentax K-500 brand new, it wouldn't cost too far from your budget.

In a word? Yes!
When it was released it was the top of the entry level DSLRs. There are now a couple of new kids on the block to usurp that title but it is still very competitive and, because it is yesterday's model, can be bought at VERY good value or money.

The D3200 is an excellent camera. Although the D3300 is now available, it only adds a few whistles and bells that won't make a real difference to you. If you can find the previous model, the D3100, you might save money and get a camera just as good.

It will be perfectly fine. Don't believe the hype. Newer cameras may have more megapixels and a few tweaks, but all DSLRs do much the same and, unless you are particularly observant, it would be hard to tell the difference between photos taken with most (consumer) DSLRs. Variability in operator performance is a lot more significant.