Osteospermums hail from southern Africa so they are too tender to reliably overwinter outdoors in the UK. When Which? Gardening magazine trialled different methods of overwintering osteospermums this is the method that worked best for us:

Taking osteospermum cuttings

Taking cuttings was our most successful method. It's easy to take softwood cuttings in
summer when osteospermums are in full growth. They root easily and grow on well. Cuttings have the disadvantage of being small plants at the start of the summer, but osteospermums grow so rapidly this won't be a problem for long. 

Caption: Taking cuttings in summer is the best way to overwinter osteospermums

Other methods we tried

Mulching osteospermums

All our plants died when they were mulched and overwintered outside. Osteospermums are also
known as Cape daisies, so their native environment is one of hot, dry weather and high sunshine. In both Yorkshire and Glasgow, they were blackened and dead by December, despite the mulch.

Lifting osteospermums and overwintering indoors

The plants that we lifted and overwintered in the greenhouse suffered indoors. Two of the three plants in Yorkshire died and the third limped on until the spring, losing leaves and becoming gradually weaker.
Those overwintered under glass in Glasgow were better, but they wilted continually and one lost all but a single stem. These plants didn't perk up when planted out in early summer. One lost its main
stem due to top-heavy growth and they all had dead leaves at the base of the plant. They were hit by grey mould, which suggests the plants were weak and susceptible to disease.