Hi,
There are several good ideas here already. I can only add a little. In particular, I'd look for a dry/worn/damaged trunnion, as Andy mentioned. In fact, if it's ever been apart, it could also be that a trunnion has been screwed back together too far, actually reaches the end of the threads as the steering reaches one extreme. (Note: The trunnion is the steering mechanism below the vertical link on each side... It's actually a large, acme-threaded screw on the vertical link, that screws into the trunnion.)
The very first thing I'd try would be to lubricate all the front steering and suspension joints. The trunnions can be difficult to get grease into, so many folks resort to injecting 90W gear oil and that's even listed in the factory service manual. Oil can be particularly helpful if a trunnion has old, dried up grease in it.
If lubrication doesn't help, each front trunnion can be isolated and checked pretty quickly and easily just by disconnecting the tie-rods at each wheel and then turning the wheels from side-to-side by hand. Go ahead and try it while the car is lifted if you wish, but for a more realistic test I'd suggest letting the car at least partially back down onto the ground, so that some or all the weight is on the suspension, then grab each tire and trying to turn it side-to-side by hand.
This test should give you an idea if one side or the other is binding and should either identify the problem or eliminate concerns about the trunnions. It could be either side binding. If so, the fix is in the trunnion. If not, it's back to looking into the steering box and the various knuckles and joints on the TR3 setup.
Next thing to do would be to re-attach the tie-rod ends and put the car up on a ramps or a drive on rack with the full weight on the suspension, but with room to get under it with a good bright light and watch all the steering mechanism work, while someone else turns the steering wheel back and forth. You might see some slop or other problem in one or more of the various joints. Alternatively, sometimes you can grab a joint while it's working, and feel the play in it... Just be careful not to get your hand pinched in the mechanisms.
It could certainly be an alignment problem, too. TRs up through the TR4 only have an adjustment for toe-in. Caster and camber aren't easily adjusted. If the car has even been in an accident or hit a curb, there can be bends to the frame or front suspension that cause misalignment. A knowledgeable frame and alignment shop might be able to realign things for you. Try to find a shop with some old-timers who know how to work on old style suspensions and frames!
Hope this helps! Let us know what you find (and what the fuel leak problem turned out to be!)
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