I'm not sure when I will manage to go and see this, but I look forward to it... It is running NOW until 22 February 2015...
From the Astronomy Photographer of the Year website:
The Royal Observatory Greenwich is proud to present the winning images of Astronomy Photographer of the Year 2014. Now open, our annual free exhibition showcases these incredible images of the sky, ranging from within our solar system to far into deep space.
Solar features, eclipses, aurorae, nebulae, star trails and more can be found in the images on display. Winning entries have come from all around the world in another record-breaking year, with more images entered than ever before. And for the first time we even received a photograph taken from the edge of space!
See also London Timeout's review of the event.