There is no statutory minimum age to travel abroad. (My friends' son used to travel regularly, unaccompanied, from his family home in Sheffield to his relatives in Paris. He was 12 at the time).
However individual carriers are free to determine their own policies on conveying unaccompanied minors and some countries won't admit unaccompanied minors unless they're met by an adult upon arrival. Additionally hoteliers can are free to set their own rules regarding the minimum age of their guests.
Eurostar will not permit children up to the age of 12 to travel on their own. Their website says that they'll
consider carrying 13 to 17 year olds but they ask that they're emailed in advance, to discuss the situation:
http://www.eurostar.com/UK/uk/leisure/travel_i nformation/before_you_go/special_travel_needs. jsp
You'd also need to check the requirements of the Elipsos Trenhotel service, who operate the 'Talgo' trains between Paris and principal Spanish cities. (Remember, as well, that Eurostar arrives at Gare du Nord but the international services to Spain leave from Gare d'Austerlitz, so you'll need to know how to get across Paris).
Rail Europe is SNCF's UK agent (and sell tickets for Eurostar and RENFE services), so they're probably the best placed to know all of the rules and regulations. You can phone them on 08448 484 064 (0900-2100, Mon-Fri. 0900-1800 Sat).
That just leaves checking with the hotel that they'll allow you to stay without an adult.
Chris