Is the Inca trail the only route to arrive at Machu Picchu by foot?

On foot, an alternative to the Inca Trail is to walk from Aguas Calientes, along the bus route. There is a checkpoint at the bridge where you have to present an entrance ticket before continuing. Walkers take the stairs that connect the switchbacks used by the buses (beware of the vehicles).

Machu Picchu Trek gives an overview of options:

The most popular trek to Machu Picchu is the Classic Inca Trail, which follows original trails that the Inca’s would have taken from the Sacred Valley to Machu Picchu. Along the way trekkers are treated to a wide variety of impressive Inca sites and stunning scenery.

Due to its popularity and concerns over the impact of tourism on the Historic Sanctuary of Machu Picchu, the trail is limited to 500 trekkers a day (300 of which are earmarked for porters and guides). Securing a place on the Inca Trail means booking early, particularly during the busiest trekking period in the dry season (May-September).

Alternatively, we highly recommend considering some of the other treks to Machu Picchu, which are all unpermitted, less touristy, often more affordable and offer unique variations on the Classic Inca Trail.

• Salkantay Trek: A great 5D/4N trekking challenge with incredible scenery. The highlight on the trek is getting up close and personal with Nevada Salkantay, the 6,271m iconic Andean peak. The second most popular trek in the region after the Inca Trail and voted one of the Top 25 Treks in the World by National Geographic
• Lares Trek: A less strenuous trekking trail that provides unrivalled opportunities to interact with local Andean communities that have changed little over the past few centuries. Undoubtedly one of the best cultural trekking experiences in the region
• Choquequirao Trek: The longest and one of the toughest treks in the region, but super rewarding. Choquequirao is an Inca site that is worthy of a visit on it’s own. Combined with Machu Picchu, this trek is fast becoming the ultimate archaeological trekking experience
• Inca jungle Trek: Designed with the adrenaline junkie in mind, the Inca Jungle trek combines a massive 60km downhill cycle with trekking, zip-lining and potential river rafting.
• Vilcabamba Trek: By far the most off-the-beaten path trek to Machu Picchu. On this trek you are guaranteed three things: absolute solitude, unbeatable alpine and jungle vistas and sore legs.
• Huchuy Qosco Trek: A short and pleasant trek to Huchuy Qosco (‘Little Cusco’ in Quechua), which is just north of Cusco, in the Sacred Valley.

Another good reference is the National Geographic article Top Six Alternate Routes to Machu Picchu by Mark Adams, author of Turn Right at Machu Picchu.

Well the key thing you're missing is by foot...from where?

If you're saying from Cusco, then yes, as Dorothy mentions, you have several alternative treks.

However you can also get the train to Aguas Calientes, and then forgo the bus ride up the mountain in the morning and walk, if you really wish to. Although I was on the first bus of the day, and we still beat the walkers up the hill - it's quite a hike, and they looked exhausted. I suspect it'd take me over 2 hours to do, if I'd walked.