When the primary winding is open circuit, you can't do much unless you can see where the break is.
Please post a hires picture of the bottom of the Transformer T51 and then another focusing on the pin 1 and 4 area.
In regards to your question, maybe someone with more knowledge of transformers could answer.
The UK mains voltage is 230Volts AC 50Hz, correct?
My best approximation is the secondary voltage is 9VAC but how many Watts is the Transformer?
I never liked halfwave power supplies as calculating the DC output voltage accurately is difficult as it depends on the load and in this case we don't really know what the load is. The load is made up of the following - It would appear that there is around 100mA of current through the Relay RY51 when it is energised - assuming the voltage on C52 doesn't change or changes very little. There would be minimal current flowing through D54 so it's safe to ignore that. IC51 Datasheet says it is good for up to 500mA so no help there. So more than 100mA but less than say 500mA?
??
If you had a variable DC power supply up to 15voltsDC, it could help. Or we knew the voltage drop across R901 on Page 10 or the voltage across C52 page 25 in PWR ON.