Moneymoo
If you have exhausted all banks and brokers in search of a joint mortgage and are unable to raise a mortgage jointly then it is unlikely that you will be able to purchase the property jointly and will have to consider the option of your BF buying the property in his own name( I would be surprised if the banks prefered one borrower over two unless there was a serious blackmark on your credit rating).
Perhaps you have not yet tried all lending institutions, if not use a broker as they will most likely be able to identify the banks most likely to approve you so one application will appear on your CB instead of multiple applications.
One suggestion from left field ,I am no expert so might not be possible, approach the builder / developer and ask if you could rent to buy. You will have to pay a bit over the odds. If you can get agreement in principle from the developer, then use your deposit money to pay off or pay down your debt on the basis that the bank then give agreement in principle for the mortgage in a period of 3 years.
Your rent will meet the deposit requirements when it comes to drawdown. WARNING These schemes do favour the banks and the developers in terms of deposit levels and purchase price and they do put your mortgage repayment date out a further 3 years but they also give you the option to not complete the purchase should your domestic situation not be as expected or the property market move significantly against you.
I would not suggest that rent to buy is a good option under normal circumstances but it may be useful to your particular situation.