How about South Africa? Or Northern Africa such as Morocco? Morocco is easy to get to from London, offers beaches and a true cultural adventure, and would not make too big of a dent in your savings account. We went as a family last year, partially because the destination is both exotic and affordable, so we were able to really do some fun things without overspending. We did a 2night/3 day tourist trip to a desert tent/camel ride/food for $80pp all in.