If it happens striclty once per revolution, then it is likely to happen exactly at the same pedal position every time. For example, "every time when the left pedal begins the downstroke".
If this is the case, it must be in the front part of the transmission, since any problem happening in the rear, will be multiplied by the gear ratio and so, it will happen at a different pedal position each time, (unless you have a 1:1 ratio).
There are a few things that can be felt like a skip that happen on the front side.
First is a damage in the bearings and cup of the crank axle. If it is a Sealed Bottom Bracket, then it may need replacing. A Cup and Cone type BB, may get away with replacing only one component, but they tend to be cheap and it is better to replace the whole system (Or even upgrade to sealed). By "a damage" I mean a dent in a cup or in the spindle.
There can be something loose. It is known for square tapper cranks that if they are used while not tight enoug, the square hole can get deformed and out of shape, alowing the crank to wiggle. It is usual though that the foot only feel one direction of the wiggle (i.e. you dont feel when it "wiggles back", usually half a revolution after the initial wiggling). Sometimes this type of damage persists even if you tighten the crank retaining bolt. I have little experience with cottered cranks, but I guess similar things happen to them.
In rare cases, a loose or missing chainring bolt can give this feeling, specially when the chain is not perfectly aligned with the affected chainring.
Yet another cause for this feeling can be a damage in the pedal. I have seen pedals where the cage is damaged in such way that in a specific position of the spindle, the cage wiggles up and down, but only in that position and not during the rest of the rotation. If this where the case, imagine what you would get if the pedal suddenly moves down a little bit during the stroke. This type of thing, however, is usually felt with just one foot, not both.
I Agree with another answer here that you should disengage the chain from the chainrings and try to pedal (while leaned into a wall or a pole, etc.) to see if you still feel the weird thing. By dropping the chain tou isolate the rest of the transmission, and if the problem can still be felt, the it has to be in the front end.