London has an extensive public transportation system with buses, the tube, and trains making it easy to get around. The quickest option between locations is to use the tube or train. For example, to go from The Shard to The Castle Climbing Center, take the Jubilee line from London Bridge to Manor House and walk 12 minutes to the center. The estimated cost of transportation for this itinerary is around £20.
If you have more time, you may want to explore more of London's adventurous activities such as zip-lining at Zip World London or kayaking on the Thames. For shorter trips, you can consider removing an activity or two from this itinerary or adding some free time to explore the areas around the attractions.