Alexander used to date Lady Louisa Cecilia Compton (the daughter of Spencer Compton, 7th Marquess of Northampton and his 4th wife, Ellen Erhardt - formerly Viscountess Cowdray and wife of Michael Pearson, 4th Viscount Cowdray). He has since been in a serious relationship with someone else.
Alexander and the Compton girls have unfortunately been subjected to a lot of rumours lately because of Louisa and Ali's not-so-amiable split and subsequent events: Louise started dating Ben Bloomfield, who had been her half-sister, Lady Emily Rose's boyfriend. Lady Emily (who is the daughter of Spencer Compton, 7th Marquess of Northampton and his 3rd wife, Rosemary Hancock), in turn, has stuck a close friendship with Ali. They have been to Mustique and Ibiza lately (although not alone, of course, but with their respective new partners and other friends). Emily now works in Ali's private investment firm.
Pippa is from their set (actually, she was more part of the 'set' than Kate, before the latter started dating William), she's very good friends with George Percy and van Cutsems, and yes, she was in Mustique and Ibiza with Ali, Emily, Charlie and the rest, but I am pretty sure she isn't dating Alexander.
On another note, Kate really does look
gorgeous in that grey dress. And
this picture of Prince William is beautiful: I love the way Kate (who is in the background) appears to be looking at William and smiling.