At that age I'd do a compression check, you just screw the gauge into
each plug hole, and crank.
What's the state of the plugs, tan, or sooty?
Two things to try, raise the tickover, just one screw on the carb,
or adjust the mixture. What did the last MOT say on the emission
printout? DIY mixture adjustment can best be done with a
Colortune (glass topped plug). As you get near correct the engine
speeds up, and runs smoother. Adjust until you are slightly
in the yellow flame region.
You don't say if it is miss firing.
With an old coil, points, distributor
system, check the plug leads with a meter, one of the five quid
digital ones with resistance ranges will do. Or just replace them.
Capacitor, and the breaker points, may be past their sell by date.
At this age the vacuum advance may be have a leaking
diaphragm. Attach a pipe and suck. The hooked spring that
moves the timing advance plate should move.
Check the timing, this is fairly critical for good running, and
although you can do a static timing, using the 5 quid meter
in voltage mode, you really need a timing light.
If it's using oil, and gives smoke on the overrun it
may be just engine wear and old age. And, once
an engine has, at sometimes in its life, been cooked
by loss of coolant, your get soft piston rings, and hardened
oil seals that leak. A not uncommon situation with
older s/h cars where you buy someone elses problem.
So what is the cars history, and did the problem
suddenly appear?

You could have an air leak into the manifold.  This will weaken the mixture
which has to be compensated by choke.

The leak could be due to:

a) split/loose/unseated brake servo vacuum hose
b) split in bake servo diaphram

To test these remove the hose from the inlet manifold and cover/seal the
inlet hole

c) vacuum advance circuit air leak.  This could be a single hose from the
carb to the distributor or you could have a complicated arrangement of hoses
which allow for different advances during engine warm-up.  Complete
overkill!  I removed all of these on my Uno.

d) cracked inlet manifold
e) broken inlet manifold to head gasket
f) broken carb to inlet manifold gasket / spacer

You almost certainly have a large brown plastic/composit spacer bewteen the
base of the carb (f).  These have been know to deteriate.  On common fault
is corner comprssion where the carb mounting studs are.  Over time,
especially with overtightening this compression results in a bowed plate AND
carb base.
This is fairly easily fixed new gaskets AND refacing of the plate and carb.
A little Hylomar (Blue non setting) gasket seal will work wonder if you have
difficulty in refacing the parts. (Don't get any Hylomar near the small
holes / channels located around the base plate to carb interface).

Finally, listen for a pssible air leak before your start.  Manully adjust
the thottle whilst listening for rushing air.  Also wet your finger a feel
for air leaks around the carb and hose interfaces.

Nick /////