The most cost-effective ways to travel from Champion Hill KCL residence to Guy's Campus several days a week are utilizing the KCL shuttle service, walking, or cycling. The KCL shuttle service is free for students, staff, and visitors, providing a convenient and direct route between the campuses. This service is highly recommended for those who prefer a straightforward and complimentary travel option. Walking and cycling are also cost-effective as they incur no monetary cost and offer health benefits. The walking distance is approximately 4 miles, taking around 60-90 minutes, while cycling takes around 20-30 minutes. These options are practical for short distances and provide flexibility in travel schedules.

For those who prefer public transportation, buses and the London Underground offer affordable and reliable options. The bus service, leveraging the £4.90 daily cap for Zones 1-2, is the most consistently affordable option for frequent travel. Several bus routes connect Champion Hill to Guy's Campus, with journey times varying between 45-60 minutes depending on traffic. The London Underground, particularly the Northern Line, provides a quicker route but at a slightly higher cost. A weekly or monthly Travelcard can significantly reduce commuting expenses for frequent travelers, offering unlimited travel on buses and trains within specified zones.

Combining different modes of transport can also be cost-effective. For instance, taking a bus part of the way and then hopping on the Tube can be a good compromise between cost and speed. This combination allows for a more flexible travel schedule while still being economical. It is important to plan your route in advance and stay informed about service updates to ensure a smooth commute.

In summary, the cheapest and most convenient options for traveling from Champion Hill KCL residence to Guy's Campus several days a week are the KCL shuttle service, walking, cycling, and utilizing public transportation with a weekly or monthly Travelcard. Each option has its pros and cons, so the best method depends on personal circumstances such as time availability, weather conditions, and fitness levels.