It could be walked in about 15 minutes.
Out of London Bridge station, across the Thames onto London Bridge itself, then bear right onto and along the A10 (Bishopsgate) until you're at Leadenhall Street, just past Leadenhall Market.
St. Mary's Axe (the street where the distinctive 'Gherkin' building is situated), branches off in a North Eastwards direction a short further distance from here.