I agree with khbuzzard. It is more likely than not that you WILL make the flight to JFK. BA would not sell that ticket if most people missed that second flight.
As for having to buy a walk-up ticket for the long-haul flight if they do miss the connection at LHR, that is not correct. These flights are on one ticket. If the flight from Zagreb is late enough that they miss the JFK flight, BA will put them on another flight at no cost ( unless they have to overnight in London, in which case the passenger pays for the hotel, I believe).
And BA will go to some lengths to prevent them missing that flight. When our connection to Barcelona was jeopardized by a late arrival of our BA flight from the US to Heathrow, we and the 20 other Barcelona-bound passengers were met at the gate and escorted to T3 and into the Fast Track lane at security.
Just make sure you do not tarry on your way to security; as long as your boarding pass is scanned in within the required time, they won't deny you boarding.
You can shorten the time it takes for disembarking the plane by paying to select your seats in advance, and choosing seats as far forward as you are allowed.