Treatment for large blue veins on the temple going under the eye? (Photo)

Thank you for the excellent images you provided. 
I recommend microphlebectomy for these and they will heal very nicely. This is our area of expertise for facial veins. Make sure you apply topical creams as the puncture wounds are healing to reduce the likelihood of hyperpigmentation - Sclerovase from VenaSmart is the one I recommend. It is non-hydroquinone based and can be imported into the UK. 
Hratch L Karamanoukian MD FACS

I would not recommend sclerotherapy (injection into the veins) of the veins near the eyes or face. The drainage of veins is invariably into the head region. Microphlebectomy may be an option. Advice searching for an experienced surgeon. 

First line approach is to use an appropriate make up base to cover them. Medical treatment can be laser ablation if they are small enough and superficial or sclerotherapy if they are larger. There are many experienced plastic surgeons in the UK you can seek consultation with. 

I have treated these types of veins very successfully with 1064 nm YAG laser.  It requires an experienced laser physician and special care needs to be taken to protect the eyes.  My patients have been very pleased with the results.  Regards,Dr. Ort

I would treat the veins that you have posted in the picture with sclerotherapy.  This may take 2 or 3 treatments but the results are excellent and the procedure is very safe to do when performed by an experienced injector.

Based on the size of the veins I would treat them with sclerotherapy, plus or minus laser or needle RF.  It may take a couple of treatments to fully resolve.  Seek out an experience vein surgeon that deals with facial veins, but overall a safe and effective treatment.  The veins are too large for laser alone, so I do not recommend that route.