Simple analysis
Scenario 1
Company offers, for eg, 1% pay rise.
Balpa negotiate and achieve, for eg, 3.1% pay rise.
Result - Your Balpa membership fee has been sorted for the rest of your time with that company - and you are still in profit.
Scenario 2
Company offer, for eg, 1 pay rise.
You have no recognition, so nothing happens.
Company changes mind and gives 1/2% and you have no choice (no collective bargaining, strike would be illegal, strike threat would be laughed at etc etc) but to accept or change jobs.
It's a no-brainer really.