Full-time British royals can't, in practical terms, have other work. They commit themselves to charitable and enabling roles and these would take priority. The civil-list is given to them to cover the cost of carrying out that work, not as a salary.
Others with a royal connection do work:- Peter and Zara Philips; the Gloucester children have worked/still work (not sure if the daughters continued to work after marriage); same with the Kent children; Lady Gabriella Windsor and Lord Frederick Windsor.
The UK press are not interested in the non-fulltime royals (with the exception of Zara because of her sporting achievements) so they never got hounded or followed by the paparazzi.
When the Duchess of Cambridge worked for Jigsaw, apparently just getting in and out of the building for all staff was near to impossible because of the press outside.
And keeping the work secret - in these days of mobiles and the willingness of the press to buy pictures and ignore privacy, I think that is next to impossible.