Perfectly possible. If you are a Roman citizen, you can go where you please. And even if you are not a citizen, you can still go where you please. There are no borders in the Empire, no checkpoints.

The "how" is simple: money. You need to get there and get settled, and that will cost, especially if you are bringing a bunch of stuff with you. Fortunately you are a merchant and no doubt have some feasible contacts for such a journey. Your route would probably be from a North African port via ship, from Carthage or Utica or somewhere in Tripolitania, or perhaps Alexandria. From there you would probably sail to the Gulf du Lyon, to port at Italica in Hispania, or Narbo / Arelate / Massilia in Gaul. Then it is overland through Gaul on the good Roman roads to the Channel, then a quick passage across to Britain from Portus Itus (near Calais) or Gesoriacum. From Lepcis Magna, central N. Africa, the trip is about 30 to 50 days total. You'd be wise to hire some guards for the overland route in Gaul, as well. Gaul is a good little Roman province by the reign of Hadrian, but any road outside civilization is dangerous at the best of times in the ancient world. Better safe than sorry.

Once you are there, it's just a matter of starting your new life by finding a service gap and filling it. You will be a stranger wherever you go, which is not ideal in the ancient world, but not insurmountable, especially if you are a Roman citizen. If you want to continue the merchant life, you will need to find an angle, develop some contacts, set up shop. The Roman army would probably be a good bet. You might even leverage your contacts back in North Africa to start up a modest import business for wild animals for the amphitheaters of Britain and Gaul. Roman demand for animals for the arena hunts and games was insatiable, especially in the High Empire.