you say the cold water tank in the loft is running low and the ballcock float is hanging low.
Therefore it is the cold supply pipe to the tank that is frozen.
This is quite normal. The tank is very large, probably made of plastic, so it takes low temperatures for a long time to freeze it. The pipes are much smaller, and probably made of copper, so can freeze quickly, especially if they are in a cold draught and not lagged.
First turn off the main stopcock. This will prevent water being supplied to the frozen pipe. The frozen pipe might have burst or come apart, in which case it would gush out water as soon as the ice melted.
Then inspect the pipe. Most likely it froze first in an area that is not properly lagged and is in a cold draught. The ice block will then have grown and extended inside the pipe. Around the eaves are most likely to be draughty, unless you have a hole in the wall. If an attempt has been made to lag the pipes, gaps are most likely to occur at the ends (e.g. next to the ballcock), at elbows (where it may gape) or where there is a fitting, such as a valve or a compression connector, that is too big for the lagging to enclose it.
Use a hairdryer (never a blowlamp, unless your fire insurance and life insurance are very good and you are tired of life) starting low down where the pipe enters the cold area, and working your way slowly along. This will allow any released pressure in the pipe to escape downward.
When looking for a burst, it's most likely that a joint will have been pushed apart by the expansion force. So examine all compression joints with a torch and your fingertips for any sign that they have opened up.