I sent cryptocurrency to the wrong wallet type
If you entered an address for a different type of coin, then there are sometimes solutions to retrieve your coins.
Bear in mind that these transactions will still be valid transactions, so in this example, there will indeed be Bitcoin that has been correctly send on the Bitcoin network. Thus, these cannot be reversed. The problem is that you don't have access to the address on the Bitcoin network to actually access the coins!
The following uses the example of you entering a Bitcoin Cash address when you should have entered a Bitcoin address.
Sometimes wallet keys are compatible across different, related coins. This would apply to Bitcoin and Bitcoin Cash (and many other Bitcoin clones), and Ethereum an Ethereum Classic. You will need to find some way to extract the private key associated with your wallet address, and then import it into the wallet.
In this case, you should go to your Bitcoin Cash wallet and look for some option to extract the private key associated with the address you used on Bittylicious. This is usually a long string of characters.
Then, in your Bitcoin wallet, you should try and find some way to import this private key.
Hopefully, possibly after a resynchronisation, you should see your correct balance.
I'm afraid we can't really help further as there are far too many combinations of cryptocurrencies and wallets for us to really offer quite and easy assistance. You'd best contact people on forums or reddit for help, but don't give your private key to anyone you do not fully trust.