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I don't think they would put you to sleep, but they can give you medication that could make the colposcopy much more pleasant for you. For most women, a colposcopy is generally mildly uncomfortable, since the cervix has fewer nerve endings than most parts of the body. However, for some women it can be significantly uncomfortable and scary. Since you've been through it before and might forego the procedure completely due to your fear, please discuss it with your doctor. He or she would prefer that you have the procedure, even if it means using medication that most women would not need. Using either oral or IV medication, it's possible that you would have the colposcopy and feel no pain and no anxiety at all. It could be similar to the medication give for a colonoscopy, which I have undergone several times with no discomfort. Best wishes.
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If your GP refuses, I would consider asking for a second opinion. I'm not sure how it works in the UK, but in the US, the doctor would not want o lose you as a patient, or you could find a doctor more sympathetic.