The newest princess born into the English monarchy is Princes Eugenie of York. She was born in 1990. Lady Louise Windsor was born in 2003 but she is titled as a lady not a princess.
The princess royal (princess anne)
Princess Anne is the firstborn daughter of the English monarch, and so is the current Princess Royal.
Princess Caraboo was born in 1791.
Princess Yukiko was born in 1680.
Princess Tarakanoff was born in 1753.
Princess Changping was born in 1629.
Princess Muneko was born in 1126.
Princess Sukeko was born in 1147.
Princess Kuniko was born in 1209.
Princess Yasuko was born in 1076.
Princess Manmati was born in 1573.
Princess Hwahyop was born in 1733.