It depends on the airline. I flew from AMS early this morning on LX, and security queues were an utter disgrace - certainly the worst I have seen at AMS for a very long time. Having arrived at the gate and last passenger to board (doors closed 1 minute behind me, and I was somewhat short of breath). As I was running to the gate, I asked if others would make it, and the gate agents said 4 people would be rebooked for free, who they thought were still in the security queues. They had waited as long as they could, but people on the aircraft had connections at ZRH so needed to get moving. Thankfully I have M&M status so was able to use priority security.

To come back on the AMS disaster, it was VERY bad this morning, and completely lacking in any sort of management of queues and passenger flows. How KLM can watch this to happen at their homebase is bewildering.

jfk-lhr-zrh all BA, 1 hour connection???
 

I was checking on AA site for a jfk-zrh RT booking, one routing listed for the outbound all on BA, jfk-lhr-zrh with a 1 hour (exactly!) connection in LHR--how is that possible?
About a year ago I flew (all BA) zrh-lhr-jfk T5-T5 connection it took over 90 minutes to get to the departing gate for LHR-JFK: even with FAST TRAK for LHR security, I had to take a train (within T5) and then walk (at a fast pace) a considerable distance to get to my departing gate. [I'm assuming jfk-lhr-zrh would be the same "set-up" but in reverse.]

1 hour connection is perfectly possible, albeit if your inbound is delayed it becomes a bit tricky. Remember you can go though connections at the satellite buildings if arriving and departing there. Lots more details in the connections guide linked to in my signature.

60 minutes is the published Minimum Connection Time for a T5-T5 connection. Generally, that's set at a level at which the airline expects that most passengers will make it to the onward flight on most days. But there's a significant level of risk if you book something that's bang on the MCT.

LHR security could be the biggest SNAFU; I was once connecting T3-T5, for T5 security they found a 10 gram tube of ointment NOT in the ZIPLOCK bag = my entire carry-on had to checked.

No problem at all - many people make 60mins T5-T5 connections everyday.