No, even the thinnest wire should work.
I would check and double check your wiring codes. The line cord wire that goes to terminal 2 of the socket is traditionally RED,
3 - BLUE and
5 - WHITE.
Note that the numbered terminals to which I refer are the screw or IDC terminals where the house wiring attaches to the socket.
Confusingly, some sockets also have numbers printed on the PCB
where the socket itself is soldered on, and these are reversed (some bizarre British Standard numbering as opposed to BT's own numbering system, I believe)
See my scrappy drawing here:
https://www.vintage-radio.net/forum/...2&d=1206469276
Then, use one of the recommended "conversion" methods for wiring the phone, you shouldn't need to invent your own!
If this still fails, try the phone on someone else's socket. It could be that yours is miswired.
Nick.