Welcome to FT!!!
This is an ongoing bug bear. On ba.com you can't be sure which fare class but there are some ways.
On short haul - economy flexible is Y - full pints and miles. Economy lowest and then upgrade using the upgrader in the payment screen to a changeable ticket and that will be B or H full miles and points. All other economy classes are 25% miles and no points.
On long haul economy you can't use the same logic as only N class is totally restricted. Y is fully flexible and the others are changeable for a fee - but only B and H get full points and miles so you have no way of chosing them as you do in shorthaul.
For Club - flexible will give you J, lowest will give you D or I.
For First - flexible will give you F, lowest will give you A.
For WT+ - flexible will give you W, lowest will give you T.