Tequila, what a helpful GP you have. 
CBT is available on NHS, at least it is here. And GPs ought to be happy to refer to CBT, it has a relatively high success rate for very few sessions, and is cheaper than other types of therapy, and non-invasive (unlike anti-depressant drugs, for instance). You can, if your surgery really won't shell out, get hold of good CBT books and cds. Let me have a google and see if I can remember what I was recommended. (If I can find it, I'll PM you and the OP.)
OP, I can completely understand what you're saying, and it's never an 'easy' phobia to have, because to so many people it just seems self-indulgent or childish. 
It is very, very hard to appreciate what it means to a needlephobe if you've never had this fear yourself. It's also one of the few phobias where you might have an extreme reaction (see vasovagal shock) while the injection or blood test is happening, which can be dangerous, so I've never understood why HCPs can be so uninformed and unsympathetic towards needlephobes. I went without dental treatment for about 15 years (yuck, I know) because of my needle phobia, and it was massively helped by a very sympathetic dentist who understood, and used local anasthetic gel and pressure to numb areas for dental injections. Now, though it's not a nice prospect, I think I could happily go to a dentist who didn't use those techniques and I'd still be ok. 
CBT is good, but you have to work at it yourself - in other words, it's a case of that old chestnut, 'you have to want to change'. I have had CBT for pregnancy anxiety (MCs) and found it very helpful. You do need to keep it up, though! CBT should help if it's a fear about the actual process you're dealing with, or sight of blood. If it's the pain, then EMLA cream (if your GP won't prescribe, you can buy it privately) or a freeze spray might help, though be aware that EMLA can sometimes constrict blood vessels and make blood tests problematic.
As a 'recovering needlephobe' 
, I can't really imagine that having an oral sedative would have helped me. It took me being pregnant to come face to face with blood tests. I was unbelievably nervous and pretty much fainting when I went into my first booking appt with DH, and jumped on the MW to get her to do the blood test first, because I knew I couldn't face any more waiting. And she did, and it was ... fine. I could not believe how much of a non-event it was. Since then, I've had two more booking-in bloods, lots and lots of bloods done during pregnancy (I had pre-eclampsia), canulas in hospital (that was horrible, I demanded EMLA cream for some but for others they just injected local first, and it didn't really do much), and finally a flu jab during my second pregnancy. The flu jab was the last big hurdle for me - I was still very scared of injections, having decided that blood tests were more or less painless and very fast, and I was lucky enough to have a very symapthetic nurse who made my lie down for it. And again, it was such a non-event I felt a bit daft.
That's not to say that I don't still have qualms about needles, and I'm never going to be relaxed about them, but I no longer will spend months and months leading up to a possible needle event fretting and worrying about it. Anyone with a phobia needs care, reassurance and understanding, not fob-offs from your GP. Phobias really can be overcome and though it's the last thing you want to hear, I found in my own case that it was exposure to injections and blood tests at first hand that made the difference. But if I'd had unsympathetic or cack-handed MWs and nurses, I think I'd have run for the hills.
Good luck, OP, and try to keep on pushing for help from your surgery. I'm sure they'll be understanding and sort something out for you. Once you take the first step in addressing it, it really does get easier, honest.