If you want beauty brands, go to Boots or Superdrug on most high streets/shopping areas. For premium brands, go to House of Fraser, Debenhams or Selfridges. If you go to Central London you can get all these stores in one place, along with smaller beauty brand boutiques in Carnaby St.
Try Barry M (Superdrug) and for UDPP go to any of the 3 department stores I mentioned.