This'll probably be too much information, but hang in there...
... the UK atomic clock signal is transmitted on 60kHz*, right at the bottom end of what used to be known as "Long Wave" It has a wavelength of 5km, which in turn means that a theoretical 1/4 wave dipole would have to be 1.25km high!
Such aerials would be a nuisance to passing aircraft, etc., so as a consequence most long wave receivers use the magnetic vector rather than the electrostatic one.
What that means is that they pickup the signal using coils (magnetic detectors) rather than long wire aerials. In practice, these coils can be very directional indeed. Despite us being in 't days of 't internet, DAB etc., You may remember being able to tune long wave and medium wave radio stations by turning the "tranny" round on the spot. That's why.
Your Anthorn time signal receiver in the clock works in just the same way. It's low enough frequency to travel well through all but the thickest of castle walls - so unless your workshop is underground there should be a usable signal, BUT the orientation of the clock (or the coil inside it) matters enormously.
So try it on the bench, and find out at which orientation it works best. Fix it to a wall orientated in roughly the same way. Worst case, just fix it up to a wall at right angles to the one it doesn't work on now. It will probably then work.
FWIW, I have a radio clock too, but it's a digital desk clock. It struggles to get a good signal in the place I like to put it, but it "flywheels" for ages without the radio signal, so occasionally I put it in a different place so it can re-sync. This takes quite a while, incidentally, because at 60kHz, the data rate is pretty slow, usually 10 minutes or so at least. If yours is a mechanical clock, it might take even longer.
So you can most probably make it work, but it might need to be on a different wall.
Hope that helps.
E.
(*in comparison, Radio 4 from Droitwich is on 198kHz, giving a theoretical 1/4 wave dipole length of 375m - still rather tall!)
PS: regarding the battery, you could use any 1.5V battery you wish - a D cell would last ages, and if you can get a 1.5V F cell it will probably outlast you!