I had a '61 MGA 1600 but that was 40-some years ago, so my (uneducated) choice back then, 20W50 Castrol, isn't necessarily relevant, The question that hasn't been asked is;
"What was the factory recommended viscosity?"
While multigrades were in their infancy then, the engineer's base viscosity recommendation could still be a useful reference. The only thing I found online was a reproduction of an MGA owner's handbook
MGA that states:
Above 32F= SAE30
32F-10F= SAE20W
Below 0F- SAE10W
or SAE 10W30 Multigrade for all temps
So, it would seem that a 30 grade was the base viscosity for an MGA used in the English/European climate and that's a good clue.
With what I know today, and with an engine in good condition in a moderate climate (not often at or near 100F), I would use/recommend a high zinc 10W30, which would translate to an easily obtained HDEO 10W30 like Shell Rotella T or Rotella T5 semi-syn. An SL rated PCMO would probably be fine as well or a PCMO with a bottle of a zinc additive.
The normal warm oil pressure is listed as 30-80 psi for the 1600 and 15-50 psi for the 1500. If I got those warm pressures with 10W30, I'd call it done. If low, I'd bump up to a 5W40 or 15W40. If I ran it often in hot weather, I might run the heavier oil 40 grade oil. Overall, a 15W40 would be an OK choice, but I generally lean toward lighter oils in moderate climates... especially if the OE manuals confirm the main grade.
Oil that is too heavy can actually hurt these engines. I had a Midget at about the same time I had the MGA and for a time I used straight grade SAE 50 in both. One snowy morning with the A, I couldn't get the engine to turn over and ended up having to put a lit Hibachi under the oil pan to warm the engine enough so it would start. In similar circumstances, the Midget turned over and started but shortly after firing, I heard a "snap." Didn't think too much of that until I noticed the oil pressure was at zero. Turns out the oil pump drive had sheared off while the pump was trying to move the honey-like 50 grade. No other harm done, but I did have to pull the engine and replace the oil pump. That's when I learned about 20W50. Obviously, this is an extreme case but it just goes to show the pitfalls of going too heavy for the climate.