Let me explain -- in the interest of simplifying things, I'm afraid I've made them more confusing.

The overall question that I have is: Where can I find information on UK immigration requirements for transit passengers -- specifically a US Citizen transiting (via LHR in this case) to TLV?

The specific route was as follows: GIG - LHR (transit) - ORY (1 week stay) - LHR (transit) - TLV - LHR (transit) - GIG.

It was cut short when attempting to board from ORY - TLV via LHR, where I was unable to board and returned to GIG via LHR.

I attempted first to board to TLV on ORY via LHR. When that didn't work, I attempted resolve the issue in LHR, even though I had changed my return to GIG due to inability to continue travel.