The earliest year of data publication on popular girls' names available at National Statistics is 1998:
http://www.statistics.gov.uk/statbase/Product.asp?vlnk=15282
and from what I can remember, the names hadn't changed drastically from those which were popular in the early 90s. I'd say from my own experience that middle-to-upper class parents tend to choose traditional or unusual classics over 'trendy' names.
Chloe,
Emily,
Sophie,
Charlotte,
Lucy,
Sarah and
Alice are all pretty safe bets.