Posted: 06/11/2015 at 08:32
Convolvulus is not very hardy and won't cope with temps below -5C or winter wet so really needs a cool, light windowsill or frost free greenhouse or cold frame to survive.
Lavender, big or small, doesn't like winter wet so may be OK in a light, sheltered spot where the pots won't get frozen or drowned. I grow mine as a low hedge in full sun along the top of a retaining wall where drainage is good and they have survived -20C but, for their first winter, they had had an entire summer season to grow big enough to cope. I lost about 5 that first winter - Hidcote variety - but the rest and the replacements have survived and thrived since.