You don't require parental permission to travel abroad.
As soon as you were 16, you had the right to walk out of your parents home and, if you so chose, never to have anything to do with them again. Even if they reported you missing, and the police found you, the police could not tell your parents where you were. You're a free agent and you can travel anywhere in the EU, except for Portugal which may refuse entry to unaccompanied people under 18 years of age. (Countries outside of the EU may also have their own restrictions).
However, since you're not yet 18, you can't enter into a legal contract - which is exactly what a holiday booking is. You'll find that most package companies won't accept your booking at all. The others will insist that your parents (or other adults) act as guarantors for the contract. One way round this is to book your flights and accommodation independently. Airlines will accept online bookings, made with a debit card, from you. (Most budget airlines accept unaccompanied minors from 14 years of age. There are often conditions regarding 14 & 15 year olds but not for 16 & 17 year olds). Similarly, most online hotel sites will accept your bookings (although it might be wisest to contact the hotel, directly, to check that they'll let you book in when you arrive).
Chris