As you obtained your car license before 1st February 2001, you can ride a 50cc ped (so that defines a maximum speed of 30 MPH) I think you will need L plates as well and you will not be able to carry a pillion passenger, as you have not got a motorcycle license!

If you think you have a full moped license I suspect the only extra two things this allows you to do is remove the plates and carry a pillion.

Martin