Trim the ends of the potatoes and cut into chips. Cook in salted boiling water for 5-6 minutes, or until just tender, then drain.
Heat the oil in a deep fat fryer to 140C/285F (CAUTION: Hot oil may be dangerous. Do not leave unattended.) Fry the chips for 8-10 minutes, then remove from the oil and set aside to drain on kitchen paper.
To serve, reheat the oil to 180C/350F and fry the chips for 4-5 minutes, or until crisp and golden-brown. Remove from the oil, set aside to drain on kitchen paper and season with salt.
Fill a frying pan with 1cm/½in water and bring to the boil. Add the lactose free butter and once it has melted, add the sliced ham and cook for 1-2 minutes.
Remove the ham slices and place onto serving plates. Season with freshly ground black pepper.
In a frying pan add a little vegetable oil and fry the eggs until cooked to your liking. Place on the serving plates, season with salt and freshly ground black pepper and serve the chips alongside.