If you have a car: drive to the Boardwalk or Beach Club and valet park ($12), then walk to the International Gateway, which allows you to enter Epcot on the World Showcase side between the UK and France.
If you don't have a car but are willing to take a cab: take a cab to accomplish the suggestion above.
Using Disney transportation: walk to the MK bus stop and wait for the bus to the Yacht/Beach, Boardwalk, and/or Swan/dolphin. Get on whichever one comes first. (it might be a combined route for all these resorts) When bus arrives, get off bus and walk to the International Gateway.
Any of these will be less walking than taking the monorail, but not that much less. The first two are the quicker options. The last is the cheapest, of course.