Don't be too sure about that! Peregrines inhabit the mountains behind me & on more than one occasion have observed them take horseshoe bats from my garden at dusk time in the summer. I since found out from the BTO that they are known to do this in the some of the cathedral sites in the UK...
Nearest puffin breeding site to Brighton is at Portland, Dorset. Should be returning to their cliff top burrows April/May time. Can be viewed easily. If in doubt about exactly where to view them ask at Portland Bird Obs. situated at the Lower [old] Lighthouse.
Had fabulous views of the peregrine when in circled around the pitch in the 44th min. Came in to roost above our heads in West Stand. Seemed a wild bird as no trusses could be seen. Made the day complete for me & Mrs BS as our lives are spent living & birding in Spain.