Jaane Aalto has corresponded with me further on Parrot Crossbill identification. I have sent the Finns a selection of the Sussex bird images and many agree with me about the concerns over the head structure and silhouette. We still need sound recordings. In every respect though, it resembles a Scottish Parrot Crossbill
Some more pictures to browse -:
A nice male Parrot here
http://koti.mbnet.fi/caligata/lintukuvat6/Loxpyt.html
A female Scottish Parrot from Abernethy
http://koti.mbnet.fi/caligata/lintukuvat6/Loxsco.html
A female Scandinavian Parrot Crossbill that does share characteristics with the Sussex female, having a forehead and a smaller bill
http://koti.mbnet.fi/caligata/lintukuvat6/Loxpyt2.html