Relevant UK travel insurance cover directly relating to Jeep Safaris is GENERALLY that you are covered, assuming you are a passenger and not working. However, you should check. Also, the "devil is in the small print" none more so than with insurance and note the following from Santander Travel Insurance:
"No sports or activities are covered if you are competing in or practising for speed or time trials, sprints or racing of any kind.
You must wear the recommended/recognised Safety Equipment for each listed activity.
You must follow any safety procedures, rules and regulations that the company providing your activity operates or which are recommended by any governing body or authority for that activity."
Those three specific stipulations will, in my opinion, nullify any cover you may have. In five years I saw countless incidents of Jeeps full of tourists racing each other, driving like idiots (like overtaking private cars, pulling in and slamming the brakes on) and very rarely did I see a Jeep with all the tourists sitting down, let alone wearing a seatbelt. If you are injured or worse and you weren't wearing a seatbelt, you may well find yourself on your own. Just a personal view but I doubt I'm far wrong.