From Longman Dictionary of Contemporary Englishwith a jumpwith a jumpBritish English if you wake, sit up etc with a jump, you do it very suddenly because you are surprised or shocked She woke with a jump, hearing a noise downstairs. → jump
Examples from the Corpus
with a jump• Rose had enrolled Gabriel, with a jump of surprise the girl admitted it.• The ceiling was so low that with a jump Matilda could nearly touch it with her finger-tips.• Waking with a jump, disorientated for a moment, Hilary stared in disbelief at the kitchen clock.• But if she got pins and needles and had to move, it woke with a jump and crept forwards again. 