[Arran]

What you will need to do is confirm that the antenna coil is actually burned out on the primary side with an Ohm meter, as well as that choke. It may be helpful to find out what is supposed to be there and what is not, if that small coil/choke is supposed to be there then it was probably a wave trap of some sort, and if it is burned out you can just bypass it if the antenna coil itself is still good. In some sets they would wind the antenna coil windings for each band on the same form which can make replacement difficult, though rewinding a broadcast band primary is a possibility unless you can find a replacement from a parts chassis.
Regards
Arran