Getting from the north-east of England to Spain, without flying, isn't impossible but it's extremely time consuming. From Newcastle, the only suitable ferry services are to either Amsterdam or Zeebrugge. The (overnight) sailing to Amsterdam takes 13 hours. Then you'd have to transfer to the train station to start a 15 hour journey to Barcelona (with several changes). (I've chosen Barcelona for my example because it's one of the closest places to Amsterdam or Zeebrugge, and because you'd probably need to travel via Barcelona to get to the Costa Brava or the Costa Dorada). The journey via Zeebrugge takes about the same time but you need to take lots of different trains (with 6 or 7 changes).
The only direct ferries from the UK to Spain operate between Plymouth & Santander and between Portsmouth & Bilbao. Both of those starting points mean extremely long journeys in the UK, before boarding the ferry for a 34 hour crossing (on the Portsmouth-Bilbao route). Once you arrive in Spain you're on the northern coast (Bay of Biscay). To get to Barcelona (which, once again, provides a reference point for the main holiday areas) you need to travel, by train, for a further 8 or 9 hours.
Looking at those options, it would seem that Newcastle to Amsterdam (and then onward by train) would be your best route but it's going to take you at least two full days of travelling in each direction.
If you want to look into it further, I'll happily provide you with information about ferries, train services and hotels but, since I might have put you off going by sea, I'll simply give you two links for now:
Newcastle-Amsterdam ferry:
http://www.dfds.co.uk/DSW/EN/TimeTable/
European rail planner:
http://reiseauskunft.bahn.de/bin/query.e