Could you perhaps post close-up photos from your UHI connector and the connector side of your BT adapter?
I'm not sure if you have understood the dual sim approach correctly. A dual SIM phone accepts two SIM cards which are typically different subscriptions from competing service providers. If you wanted to use a SIM card on the BT adapter (you would not be using its bluetooth feature in this case at all), you should have the dual SIM service, two SIM cards from one and the same service provider and not only that, the SIM cards should be prepared to use the same telephone number (when someone calls you, both phones ring and you can answer from whichever you like. When you place a call, the other party will see a call from the same number irrespectively of the phone/SIM card that you called from.
Now if you were to make use of that bluetooth feature, you cannot put a SIM card to that BT adapter at all. You will need a BT SAP capable phone (in practise all Nokia phones, except Meego and Windows phones, most Android phones should work now, see other threads at the forum about Android BT SAP support, some Blackberry phones may work too although usually with the later BT SAP adapter model only...).
This BT adapter is a GSM phone that makes use of the SIM card from another phone (via BT, after appropriate security measures). The adapter/phone is not SIM locked and as such accepts SIM cards from any service provider. The only restriction should be that usually "3" does not accept these single mode, dual band GSM phones because they don't have their own GSM network (technically it would work but the phone would use another operator always, even if 3 had their own 3G coverage in that area).
This device that grumpyoldgit showed would support BT HF profile and would work (via BT) with almost any phone (both have their advantages and disadvantages, myself I'm using another BT SAP adapter model now with dual SIM service when I changed to a WIN8 phone).