The bank account that the rental income is paid into is not relevant to determining who pays the tax on it. In order to allocate the rental income to your son either partially or completely, he would need to have an ownership interest in the property as you will read here. He would need to be registered for self-assessment by completing a form SA1 and sending it to HMRC. There is no need for him to be a sole trader. He doesn't need to be claiming tax credits.
The problem with making a gift of a share in the property to your son is the potental liability to Capital Gains Tax. Such a gift would be deemed to have been made at the opan market value. However, if you gifted a very small share, then CGT may not be an issue. The gift would also be a potentially exempt transfer for Inheritance Tax purposes which would remain in yiour estate for sevn years after it is made.
I hope this helps but let me know if you have any further questions.