I have ampliobia and am effectively monocular. Monocular pilots are not, in fact, uncommon.
There are two possible routes.
You cannot do anything under JAR
You can, however, get up to a Class 1 FAA medical if monocular - there are quite a few monocular FAA ATPLs, as over there they have a system of "SODAS" - Statements of Demonstrated Ability - basically, if you can demonstrate that your are safe, you can fly.
If you are just interested in private flying that you can get an NPPL. Of course, this is just day VFR only but it may change in the future.
There are two levels of NPPL medical. If you reach the standard for ordinary drivers (Class 1) which would include the monocular, then you can fly solo. If you reach the standard for HGV drivers (Class 2) then you can take passengers. Class 2 HGV licences are not available to monocular people BUT, I like to think in response to a suggestion from me during the NPPL consultation period, a Class 2 type NPPL medical IS available to monocular pilots if they complete a satsifactory test flight at the end of their training.
It is interesting to note that the reason for this, specifically given in the notes for guidance with reference to NPPL medicals promulgated by the CAA is that "monocularity is not inconsistent with safe flight".
Having been monocular all my life I agree with this. I can play squash and tennis pretty well and have no problem with depth perception. I imagine, however, that a person used to binocular vision would find it hard to adapt if suddenly deprived of the sight in one eye.