UPDATE -
Just spoken to the head of this department for NE in Bristol. They are currently undergoing a review, the extent of which is that they will NOT be processing or persuing any action on behalf of farmers in respect to rabbit damage.
So, Natural England will NOT be isuing any notices to landowners, meaning that if the owner of the land fails to take action, then there is only one course of action. AFAIK, you need to (and this is not legal advice):
0) Check your facts.
1) Ask the landowner to sort it.
2) Write to them, and CC your land agent, mentioning your previous conversation, stating any damages (with evidence) and citing the Pests Act 1954.
3) In a month (you need to allow reasonable time to respond) you need to write again, this time CC your solicitor, stating that unless you get immediate action then you will be taking further action in the form of requesting that the Secretary of State for Environment (Hillary Benn) issue a notice to take the relevent action under the Ag Act. It ought be pointed out at this point that their failure to take action would make them liable for prosection, and that the Secreatry of State can have third party contractors enter the land to take said action AND then bill the occupier.
4) See what happens. It should be noted that once you have the above done, if you get any sort of action taken against the occupier, you would be quite able to claim damages for your crop dammage from the occupier (thats why you get evidence and CC your agent). Unless you had given them time and warned them, then your chances of getting any damages will be very slim - once you have some action from the Secreatry of State, then you could have a prima facie case for negligence occuring actual loss.
Actually, I could write an article for FW for this if anyone is interested. I'm not a lawyer but I have plenty of free time to gather the facts.