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.