British people over 50, why do some add an "up" or "on" after a verb , such as wait on, rather than wait for, while ordering, or park up on a street,

Can't speak for the British but here parking up the street means parking at a distance. Parking on the street implies parking nearby. Wait up is asking someeone to pause long enough for you to walk with them. Wait on means serving them like a waiter in an eatery.