If the frame/chassis has been replaced, that's great news. If you can, get it up in the air and confirm. Check especially for any bends or kinks where the front a-arms attach. Check all the arms are straight and true. Check all the bushings. With the weight off, move the top of each rear wheel in and out. There should be no play. If there is, figure out where. Bushings are easily changed, u-joints a little harder but play between the inner half-shaft yoke and the transaxle may be serious.
Check compression (should be high as the CR is 10.25:1), clutch release height, transaxle for noise, in other words all the usual things. Engines are not powerful but are smooth, quiet and love to rev. Original carbs problematic. Commonly switched to a Weber.
Gearshift mech is long and complicated, and prone to wear. Parts are available but can be a pain to fit.
Check door hinges for play/drop. Hinge replacement can be challenging usually requiring two more hands than you have available. DO NOT LEAN ON THE DOORS EVER !! Shoot people if they do so.
Body work and paint is expensive and time consuming to do right.
Ashtrays are rare and expensive.
Usual British car electrical issues with poor connections, cheap switches and bodged repairs by previous owners. It actually all works pretty well if left stock and proper repairs performed.
Seat frames and slides rust out.
Door windows are slow to open or close.
DO NOT TOW THE CAR BACKWARDS !! The rear latch is weak. Strong wind pressure will cause it to slip out of place, the rear cover to open, fold itself over the roof and smash the windshield. This is the fastest way to take a 100 point car and make it a wreck.
Almost everything is available. Most cheap but some $$$.
Hope it checks out. Post photos if you are able!