Jersey is not in the UK, if that makes any difference
You can travel freely from one terminal to another at Heathrow, should you have a burning desire to do so. Getting onto an aeroplane or ‘airside’ is a different matter.
To get your free passport, arrive in a rubber dinghy. That though may require you going to France or Belgium first, which is where the cunning plan falls down. You’ll need to think outside the box…. Try the Isle of Wight, though the ferries are expensive or charter King Rat and his canal coracle thing, to drop you off a couple of hundred yards off Ramsgate. Then just make sure you paddle the right way…. Best done by following the several hundred swarthy males making the same crossing each hour.