Can someone explain this as it cannot be this easy to profit by simply transferring coins between exchanges to sell at a higher price...
Indeed. The coins you are referring to probably have a really low liquidity ( volume ), which is the reason why they're priced so differently on different markets. As a result of that you may or may not be able to sell the coins, or move them fast enough to make a profit.
What you are trying to do is called "Arbitrage". See https://www.investopedia.com/terms/a/arbitrage.asp
AdolfinWolf, I think you may be misunderstanding. orssonlack is talking about the difference in price across exchanges for a single coin, i.e., Bitcoin price across the exchanges can vary. orssonlack is saying that difference is +/- 30%, he hasn't provided evidence so we don't know which exchanges he's referring to, but the reason for the swing is anything BUT really low liquidity. The fact that we're talking about the same coin means the liquidity is the same, regardless of the exchange.
S. Korea and Africa have had notoriously high prices for Bitcoin.
Presumeably you could transfer bitcoin from one exchange in the UK (with a "normal" price) to an exchange in S. Korea (with a high price) and benefit form selling that bitcoin on the S. Korea exchange for a more stable currency, i.e., Ether or Ripple. Then repatriate that Ether/Ripple back to your home exchange. It is, theoretically, that easy. But I'm not factoring in actual prices and the fees associated with each transaction. It's the fees that'll churn your arbitrage opportunity away.
To the OP, you should provide some analysis. On the same day, with in the same 10 minute period, record the price of Bitcoin across several exchanges. Post them on this site. Then let's talk about how anyone could take advantage of the arbitrage, in real terms.