You should have the side entry cap on that model. If so I believe the wires are retained by needle screws from the interior of the cap. Remove the cap and look up underneath, you should see 7 screws, one for each plug wire and one for the coil lead. If you back each of the screws out several turns you should be able to remove that wire and replace, tighten the screw and move on to the next one. These don't have to be extremely tight, don't want to damage the cap, just snug enough so the needle will pierce the wire to the core to establish a good connection.
"Disclaimer, this is a bit of a guess, haven't worked on the big Healey cap, but my Vertex magneto had a similar setup."
'73 Midget (V6)
'59 MGA (I6) under construction
'73 Lotus Europa
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