The burden of satisfying any copyright is on the user of the copyrighted material. If the publisher failed to obtain a license from you, then you have a copyright violation.

If you gave them permission but failed to clearly state the terms, then you may have a legal gray area.

Rather than invoicing for unauthorized use, I would consult with an intellectual property attorney to discuss a strategy for your recovery of damages.

I would suggest that you compile the emails into a document, and create a timeline of your interaction with the publisher, annotated with the events as you see them. Then you are armed for an efficient interaction with an intellectual property attorney.

I cannot advise you on copyright enforcement process in UK, you will need the services of a local intellectual property attorney.

You might consider after you assemble your email compilation and timeline, approaching the publisher, and letting him know that you consider his use to be a copyright violation. He may settle with you for X. But I think that is a poor strategy, and since this matter has gone this far, engaging an attorney would be best. Undoubtedly you were interested in the credit, which had value to you. Lacking that credit, and with no ability to have the work republished with that credit, you must determine what compensation would be appropriate in lieu of that credit. For example, your compensation might not be the small value provided for stock photo use, but rather a larger value which compensates one for the opportunity, creativity, technical execution or whatever was utilized in capturing and expressing the moment of your image.