EDIT: I can transfer funds from my Blockchain wallet to Breadwallet (they have the same 12-word recovery key), but they seem to be two completely different wallets?
if you go here: https://iancoleman.github.io/bip39/
generate a random 12 word seed... (NOTE: DO NOT put your seed into the online version of that page!) and then in the Derivation Path section, select BIP32 and then blockchain.info as the "Client" you will see they use path m/44'/0'/0'... whereas bitcoin core uses m/0'/0' and multiBit HD uses m/0'/0.
If you change from one client to another, you can see the Derived addresses at the bottom of the page change... even though you're using the same 12 word seed.
So, unless Breadwallet uses the same Derivation Path (apparently it doesn't) or if it allows you to specify the Derivation Path (fairly sure it won't), then you won't be able to just import the seed from blockchain.info... what you'll need to do, is create an offline copy of that BIP39 website (instructions at the bottom of the page)... put in your blockchain.info seed, select BIP32 and blockchain.info... and get a list of all the addresses and private keys... and then import all the keys for those addresses into Breadwallet...
The first section here might explain it better: https://github.com/OmniLayer/omniwallet/wiki/Exporting-Private-Key-from-Blockchain.info-and-Importing-to-Omniwallet.org
Thank you for your reply - this makes a lot of sense to why my funds will only appear on some clients, if the encryption isn't all the same. I will try to export my fund to an offline copy and see if I can import them into Breadwallet instead. Thanks.