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As the car is pretty light I would think that the dimension you mentioned are plenty strong enough - in fact probably overkill.
If there are no other attachments to the tca along its length (e.g. a compression strut or an anti toll bar pickup) which would add bending loads and if the tca has ball joints at both ends (i.e. a rodend or similar on the inner end as well as the ball joint at the outer end) I think you would be safe to go considerably lighter as the tca will be acting simply in compression and tension.
A 1" or 25mm dia 14 gauge tube (2mm wall) would be fine. If you look at single seater and clubmans chassis they would prbably be using 3/4" or 19mm tube of 16 gauge or thinner wall.
But use cold drawn seamless tube, not erw.
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