I bought the phone second hand and the account that locks the phone is not mine and I have no way of unlocking it

You need to be able to contact the previous owner to have them log out of iCloud or go to https://www.icloud.com/find/ My Phone and erase the device, then remove it from their account. If you can’t do that, the device is useless. Apple won't unlock it.

Turn off Activation Lock - Apple Support.     

I don't believe there is any way of unlocking the phone without the original owners log in details