Depending on the particular wheel you use, and its offset, you can stuff a 195 in there. The real question is WHY? Unless you do some suspension modification to this machine, it really can't use much more tyre than was on it at delivery.
There is also a question of safety here. The MGA front swivel axles are known to break under extra load. When these cars came out, the loads that could be put on the tyre/suspension were fairly low because of the non-radial, fairly skinny (155 section) tyres. Just installing 165 radials ups this load a bunch. Going to a modern high performance tyre will REALLY strain things.
I'm building a bit of a hot rod MGA myself, and the first thing I did was to upgrade to MGB front suspension. This is fairly easy to do if you have a pair of shocks customized by World Wide Auto (MGA shocks with upside-down MGB shock arms installed) The price is quite reasonable, and the shocks will be fresh and rebuilt with really superior parts. You'll also need the longer "negative camber" lower A-arms sold for Bs. Other than that, everything is straight MGB. The really neat thing here is that you wind up with front disc brakes! There are articles on the web about this. Find one and check my information. You won't be sorry.
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon