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.