I made a lot of assumptions, so I will list them here
1) The London eye is a circle
2) The London eye moves at a constant rate
3) The ground between the London Eye and Big Ben is considered level enough that other considerations are negligable (such as the curvature of earth)
4) Correct me at any time
I drew a picture; I'll leave it to you to verify the easy calculations. I would say that solving for the unknown angle PMR would be sufficient. Divide the unknown angle into 360 and you would get the proportion of time it takes to rotate along that arc. Finally multiply that proportion by 30 minutes.