Depends upon which jasmine it is. There are (at least) two hardy jasmines
Jasminum nudiflorum is the yellow-flowered winter jasmine now in flower in gardens (or going over) which is, obviously, very hardy. The white (or pinkish)
J. officinale summer-flowering summer jasmine is certainly hardy in London.
However J. polyanthum the sweetly-scented, white flowered jasmine which is sold by garden centres &c at this time of year is not reliably hardy in UK winters.
Having said that, I did get one to grow for several years in a very sheltered site in London - it finally succumbed to a very cold winter (perhaps would have done better if I'd given it extra protection?). I should also say that it didn't flower outdoors ....
