Although I don't have experience with LDN, I know that generally in the UK conflicting medications will not be prescribed together. Was the person who prescribed the LDN aware you are taking codine? In Wales at least, the computer system used in GPs and hospitals is designed to prevent the prescription of conflicting medications. If the computer system has a record of someone having one medication (for example, ibprophen) it will flash red if an interacting drug (for example, aspirin) is prescribed at a later date. This is not an absolute guarantee though.
I have tried to look it up, but I can't find anything of much use, LDN is still a relatively uncommon treatment, especially in the UK.
If it was me, I would call my GI and ask them if it is ok to take the two medications together, or i would go and have a chat to my pharmacist, they are usually pretty good at noticing possible interactions in my experience.
Of course, if the LDN does its job, you shouldn't be needing the codine for too much longer anyway as you should start to feel better.