Bank won't let me do a chargeback?

I bought a phone on craigslist for £400 for a iphone 6 32gb and I did a bank transfer however the seller isn't responding after I have sent them the payment.

I went to my bank and asked to do a chargeback but they said they can't do a chargeback

Why can't they? How can I make my bank do a chargeback on my card?

When you do a bank transfer you are paying cash.

A charge-back is for a credit card transaction, not a cash transaction. The bank can't just take back your cash payment from someone else's account.

Bank transfers are NOT credit card charges. You told them to transfer the money. They can't go to the other bank and say give us our money back. You only get the benefit if you use a credit card.

Why would you ever buy something pn Craigslist and not complete the transaction in person? You can't make the bank do anything

You can't do a chargebank on a bank transfer.

Chargebacks can only be applied when the original payment went through on a card.

Contact the police. Don't expect to get anything back. They probably used a hijacked bank account to receive your 400.