I've been seeing a chiropractor since 13 weeks this pregnancy (my third) had SPD with my first towards the end but never mentioned it to anyone as I thought it was just 'being pregnant', which it most certainly is not. 2nd time around I did a bit of internet searching too when the familiar aches, grinding bones sensation and shooting pains came on around 16 weeks. I was diagnosed with SPD by midwife and GP and had to do a self referral to physio clinic at our local hospital. They were worse than useless.
My recommendation to you, if you can afford it, would be to forget about NHS physio services or getting your GP to understand/accept what's wrong and go straight to a chiropractor who has an interest in pregnancy related conditions.
There obviously are some good NHS physios but the two I saw at our local hospital clinic were clueless about the condition and offered nothing except a support belt (which they didn't even know how to fit), an excercise sheet full of excercises I couldn't do (they didn't even bother to demonstrate the exercises or ask me to attempt them) and a cheery 'see you again if you need crutches' as a goodbye 
My chiropractor on the other hand has been wonderful and says SPD/PGP, call it what you will, is very treatable. She sees no reason why I should end up with crutches or in a wheelchair. And since I've been seeing her my symptoms have been minimised to more than cope-able levels. I have every confidence she'll be able to keep me stable enough to cope with my other two DCs both under 4yrs.
If you can't afford to see a private chiropractor (roughly £50 for 1st session and £30 for each subsequent session) then please do go back to your GP - or another in the practice and don't give up until someone treats you as you ought to be treated.
It's an absolute disgrace that so many women are being failed in this way by the NHS who would rather hand out crutches than offer proper treatment.
(Can you tell this is a particular bug-bear of mine?!!)
Best wishes with your pregnancy x