Leng grew up in Scarborough, North Yorkshire. She spent her childhood on the cliffs and beaches of the Lower Jurassic.  Leng studied geology for GCSE and A Level. At Sixth Form College she took a field trip to Ravenscar and described finding an ammonite which hooked her into geology. She studied for a BSc in Earth Science at Oxford Polytechnic, gained her PhD at Aberystwyth University in 1990, then moved to the British Geological Survey to work in the isotope laboratory.