Sounds fun! I’m biased because I work by Sloane Square so the below are my preferences -
Zara at Duke of York Square is very good and there are various other brands and stores adjacent - Massimo Dutti, Whistles, Boden, Cos.
Duke of York Square is on the Kings Road which has other newish brands like Rixo, Cefinn, Essentiel Antwerp
Duke of York Square is also adjacent to Sloane Sq tube and that is by Sloane Street for higher end brands - Maje, red Valentino, and other luxe brands.
For coffee during shopping, Pavilion Road is cute and English and fun, 1 min from Sloane Sq too. (There is an amazing stationary shop there too!)
Peter Jones a massive and well loved department store is on Sloane Square too.