Hi the Rastro or Flea Market is at the top end of Passeig Prim just before the big roundabout near the indoor market.
Its on every Saturday and BHols sometimes. They advertise these on the stall the week before.
8.30am ish to 2pm ish. If you love rummaging then its all there.
furniture, Glass, lamps, old mobiles and all the electrical bits. Plus lots of rubbish too.
No UK food or goods, except one English guy with Antiques at the top end. Lots of Spanish collectors stalls ie bottle tops books and old wine labels.
Plenty of parking.

There is also one every Sunday morning in Tarragona. It is based in the streets around the cathederal. Due to the very narrow streets, it is more, a shopping trolley/ cart  sale. much the same goods as Reus, but less antiques and more TaT. if thats possible.