As long as you are taking your full 52 weeks of adoption leave, you do not need to give any notice that you are returning to work at the end of your leave, and you can simply turn up at work on the day that you are due back. However, you might find it helpful, and it is good practice, to contact your employer just to make sure that they know you're coming back and to make any necessary arrangements.
If you are taking your full 52-week entitlement, you must return to work on the day after the last day of the 52-week leave period. You must give your employer eight weeks' notice of your intention to return if you want to return earlier than this. If you fail to give eight weeks' notice, your employer can delay your return for eight weeks and, if you work during this period for your employer, they can refuse to pay you.