I've just done the dreaded JFK-LHR route with onward connecting flight to LBA (Leeds). I can tell you from first hand experience that the Immigration hall does indeed have 3 lines. One for UK/EEA, a second for Visa holders and a third for all other passports. I can also report that the carry on restrictions are strictly enforced. For those asking 2 hours is not a long enough layover if you're arriving to Heathrow from JFK. You should count on both a late departure and a late arrival and as such I would budget at least 4 hours. Just a word to the wise.

Thanks to all who helped me plan ahead.

JFK is notorious for late departures. If you have a LHR connection from another terminal, I would have to agree on the 4 hours.

We are flying British Air from Dulles to Heathrow then on to Rome (also on BA) I have been told twice by BA that our bags will be checked thru and that 2 hours is enough time to go from Terminal 4 to Term 1 and thru security to catch the Rome flight. Do you think that is true? Thanks!!

Yup, that's what they tell you.

Check the on-time record from Dulles. I'm sure they don't have the traffic that JFK does. If your flight departs on time, it should arrive early, with the tail winds.

Just a word to the wise - you don't pass through immigration at Heathrow if you are travelling onwards except within the UK & Ireland