International Transfer at Heathrow with Separate Tickets

I made a similar journey last year, Denver to Heathrow, no checked luggage, and a separate 2nd ticket (not a connection on the same ticket) to Krakow. I moved along Heathrow's "transfer path" and do not have a passport stamp from Heathrow. I do have one from Krakow.

I arrived at Terminal 3 and walked a long way to catch the transfer bus to Terminal 5. A LONG way. At Terminal 5 I checked in at the airline desk to get boarding pass and then went through security. Very similar to this:
https://www.heathrow.com/flight-connections/connections-video

I chose some flights similar to your description and they give this connection plan:
https://www.heathrow.com/flight-connections/personal-connection-planner/UA923/BA7061/17-SEP-2019/17-SEP-2019/5/7D

Returning to Heathrow (on the separate ticket) I did check a bag and, in that case, I went through Heathrow immigration and received a passport stamp. Then I went to the airline desk to check into my flight on the ticket from LHR back to Denver.

Thank you so much for the detailed reply. I was worried that if I went directly from Terminal 2 to Terminal 5 following the transfer path that I would have problems checking in for the Madrid flight if I hadn't updated my passport through epassport immigration process. So you didn't have to even document your entry between those flights? Great response.

So you didn't have to even document your entry between those flights?
On my outward journey it is as if I didn't enter the UK, which I suppose officially, I did not. As far as my passport is concerned, I entered in Krakow. I glanced back at my photos and can confirm that I arrived at T3 and followed transfers to take the bus to T5. You do go through security again at the departure terminal.

On the way back, because of the checked bag, I did enter the UK through immigration and have the passport stamp. The Heathrow immigration official hesitated a moment when I answered his question to say that I was only staying in the UK for a few hours. When I told him I had checked bags on 2 separate tickets he nodded, stamped my passport and waved me through.

Very thorough answer. Many thanks!

You will need to be checked in and have your boarding pass for the Madrid flight in hand to go through security in T5.

Are you doing this trip before or after Oct 31? So hard to say what could happen with Brexit, but that’s something to keep a close eye on. It’s hard to predict how that could impact layovers, connections between Europe, etc if it goes through, particularly as a hard exit.

It's possible that United can issue your boarding passes in LAX for your LHR-MAD flight. Call them and ask. Even if they say no or you can't get an answer, ask when you check in. That will save you time and hassle at LHR.

It surprised me to find this out. I flew El Al to Warsaw, then on a separate ticket to Gdansk on Lot. When I left TLV, my entire route was on the computer, they checked by bag through to Gdansk and gave me both boarding passes.

Thanks to all. Arrive in LHR on 10/18 and depart on 10/28. It seemed like a very good idea to get out before Brexit :)