If you worry about it, you will get busted, even though I also have never seen a tape measure.

I too would go the 2 bag route, even with the understanding and expectation that at least 150% of your checked luggage will disappear at LHR.

And if you are thinking about carrying on, think again. Please be warned that the UK has a strictly enforced 1 (and I mean 1) carry on policy with an even more strictly enforced luggage sizer at security. If it doesn't "measure up", you WILL be forced to go back to check in, which will be a zoo, and check any extra luggage. Don't be fooled. While their version of TSA wear sweaters that say "We're here to help", it's a lie. Expect more empathy and flexibility from an SS prison guard.

LHR (and LGW to a lesser degree) should have a sign above entrance similar to Hades: "Abandon all hope ye who enter here."

Rant over. And before you flame away, I understand its their country and their rules. I also understand that I don't have to like it, or even go there.