I'm guessing Eastbourne, United Kingdom and not Eastbourne, New Zealand?– ThunderforgeNov 28, 2017 at 3:23
The order I believe it is the order of Grey Nuns (of the Sacred Heart).
Here is a US branch with an image with a similar headpiece.
Here are a few different orders but the leftmost is a Grey Nun with a heart-shaped headpiece.
This is the original posting of that image but there aren't any details besides those given by OP.
@MattGutting found a nun who disagrees with me (I am not certain in my answer so it is definitely possible). She says:
Def not Gray Nuns. They have more of a widow's peak looking thing. Could be Sisters of Christian Charity of St Elizabeth w/ modified neck piece. They may be an order unique to the UK, however. The ones that tend to have the "heart" facepiece are usually some form of "Charity" nun.
On the other hand, at least one nun disagrees - twitter.com/sisterb24/status/935580308208078848 Dec 1, 2017 at 23:14