All of the braking light system lights go on when I am driving. on 2003 Land Rover Discovery

I have replaced the back brakes thinking that would fix the problem but it still continues to happen. It drives fine but as I am driving it will start binging and then all the braking system and towing system lights will come on and stay on.

what components have you changed? may not be components, but the brake fluid or possibly the brake line. should take sample of brake fluid, check color. should be transparent. if not then due for change. review when brakes were changed with tech. ask him specifically if he had any problems. were the pads worn unevenly? did he have any issues releasing the caliper?
possible also that there is an issue with the break line itself. get thorough brake inspection as it is a safety issue.
Thank you. It is a Land Rover Discovery and from what I am seeing on the internet others have had this issue as well and they say it has to do with the ABS system. We have only had this car 2 years and we just now replace the back brakes. We had a friend who was a mechanic do it at home. I don't know if he checked the brake fluid or not. I will ask him to do so and see if that may help. Others told me the differentials needed to be changed because they were foamy. Not sure if I agree with that either. Thanks for the advice. I will look into it.
differentials should serviced once a year. they have nothing to do with brake system. may want to run the VIN# and check if any recalls on that item.
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It may be your ABS wheel sensors. Common Discovery issue.