Does removing spider veins by injections work better than laser for dark skin? It's very expensive though. (Photo)

Either sclerotherapy or cosmetic laser has potential for hyperpigmentation.I recommend that you use some topicals to reduce the likelihood of hyperpigmentation with Sclerovase and Scleroquin plus.H Karamanoukian MD FACS
certified vein specialist (ABVLM) and double board certified surgeon

Laser treatment for thread veins gives a better result on fair skin. However, there is a special laser for dark skin but it is quite expensive and will be more than £500. You can have a very good result by microsclerotherapy or veinwave treatment depending on the size of the spider veins. 

Based on your photos, sclerotherapy would probably work better.  Most lasers work on pigment, so you are more likely to get burned to be effective on veins, or get an ineffective result.Sclerotherapy works by injecting a medication directly into the veins.  Somebody skilled with this should be seen, as well as someone familiar with darker skin like yours.  In my experience, your skin type is prone to staining, or discoloration from sclerotherapy.  I would recommend someone who would follow up in 1-2 weeks to check the veins, and again in 6-8 weeks.  Sometimes blood becomes trapped, and this increases the risk of staining from the blood pigments.1000 pounds seems high, but I am in the states.  Our treatment runs $300 a session, and you might need 2 or more depending on how well the veins respond.