So I bought some Bitcoins from CoinCorner with a purchase in mind. I sent £50 each in BTC to an Electrum wallet and a Bitcoin Core, on Linux, on a decent machine. Both wallets are now synchronising endlessly. The Bitcoin Core one is telling me that it will take 12 days. That sometimes increases to six weeks. I've googled and it seems that a lot of folk are reporting insane sync times... When can I expect to see my money? 
As far as Electrum goes, its a lightweight wallet, meaning it won't take that long for it to synchronized as you don't need download the current Bitcoin blockchain size. As for Bitcoin core, its different though, there is a way called pruning. wherein it will allows one to run a smaller version of full blockchain. For technical questions for Electrum, you can go visit this board: Electrum. For Bitcoin Core, you can post your questions here, Development & Technical Discussion. @bL4nkcode, have said, don't worry about your money, you just need to wait until it goes full sync.