Various banks and building societies have different policies on how they approve transactions, and it should be possible to find one that fits your needs better. Often the first transaction to a new payee is treated more stringently than subsequent transactions. There's no reason you shouldn't ask how this works as part of deciding whether to move to a particular institution.
For example I bank with Lloyds, who currently authorise the first transaction with a new payee via text message, but after that will only require a password for further transactions with that payee.