Standard suspension should be quite soft & comfortable. If you feel the problem is just affecting the front O/S, it could be a faulty shock absorber, even if it is nearly new! I note that you say it feels OK if you bounce that corner, but bear in mind that out on the road the shock absorber will be subject to much greater & sudden impacts from the road surface, if the valving in the shock is defective it may not be reacting properly in road conditions.
The "standard" shocks that you get these days from Rimmers & others are not original manufacturer (which I think was Monroe and/or Armstrong), but pattern parts from India or China, much of the TR7 stuff is made by County, which I think is made in India. With some of this stuff there have been reports of quality issues, such as TR7 carb rubber mounts that split in a few months, or the gearbox rubber mounting which are far too hard compared to the original spec and transmit too much noise through the drivetrain.
Having said that I have Rimmers standard shocks in the front of my TR8 (all I could afford at the time!), I put them in after I found both the KYB front inserts that were in the car were leaking. For a couple of years they have so far been trouble free.
Anyway, you may be faced with stripping down that strut to check the shock absorber. If you frequent autojumbles and the like keep your eyes out for some NOS inserts, they do appear from time to time. Unipart GDA3000 or TKC1212, Monroe MR848, Armstrong RC629. Or of course modern replacements like Spax, Gaz or KYB.
Tony

<font size="1">1981 TR7 FHC Cavalry Blue
1980 TR7V8 DHC Jaguar Regency Red - sadly sold!
1977 TR8 FHC EFI Factory development car Inca Yellow</font id="size1">