Do we need an Electronic Travel Authorization to transfer planes

You haven't provided enough information to answer the question - which airport (England has many) and is your flight a genuine connection (ie is it In one booking/PNR)?

It doesn't matter whether you leave the airport, you need an ETA or visa unless it's an airside connection. Only Heathrow and Manchester offer airside connections.

If you are flying from the United States and you are going to Croatia with a layover at Heathrow and it’s all on the same ticket, then no, you do not need to get the ETA.

Just flew last month from California through LHR to go to Dublin. Yes you need the UK visa thing now. Even for transfers. Be sure to print off your approval. The website said my visa would electronically attached to my passport. When I went to check in at the British Airways counter, they asked to see my approval. Luckily I had kept the email with the approval and showed it to the counter agent. The counter agent suggested we print off the approval email because there have been some glitches getting the visa attached to a person's passport.

Just flew last month from California through LHR to go to Dublin.

Your case was different, you were entering the Common Travel Area between the UK and Ireland, which required you to go through immigration in London, then on to Dublin, so yeah, you needed an ETA.

In the OPs case, if they are in transit, going to the Schengen area, do not go through immigration, then no ETA needed.

Personally, I think I'd get one. What if your plane is cancelled/delayed or worse, and you need to stay overnight in England? Now, most people can get them approved fairly quickly, but my recollection is my husband's took about 14 hours.

"Yes you need the UK visa thing now"

Apologies for nitpicking (sorry!), but an ETA and a visa are two different things. An ETA is issued to holders of visa-waiver countries and is a permission to travel, not a visa.

A visa is issued either because you are a national of a country that is not on the visa-waiver list, or because you need a visa for work/study/living etc. In that case you don't require an ETA.

You do not need an ETA for your trip as long as the airport you are transiting is Heathrow or Manchester.

Some people here think that if you fly anywhere in the world and might be hijacked to the UK or diverted, that you will be put in front of a firing squad if you don't have an ETA.

Even if your flight is delayed, cancelled and you are forced to enter the UK, you won't have a problem. The ETA is not approval to enter. It just authorizes someone headed for the UK to get on the plane. Many people don't understand that.

You are not headed to the UK. You are headed to Croatia. You just happen to be connecting in the UK.

I do understand what the ETA is for. In the last couple years, I've needed NZeta for New Zealand (essentially an ETA) and ETAs for Australia and England. In planning these trips, I've been on multiple forums where the ETA and similar have been discussed. There were enough situations that came up, that I personally would get the ETA even if I was just connecting thru the country. Does the OP NEED one. No. Might it be helpful in certain situations, quite possibly. And no, I don't think a person without an ETA would be put in front of a firing squad or even in jail.

When the war in the middle east started, I know of folks that were supposed to just connect through Sydney that were stuck in Sydney at the airport due to cancellations and were working on getting ETAs so they could go to a hotel.

I'd get it. You might not need it, but what if you got stuck at the airport for some reason and wanted to leave? It's better to have it and not need it than need it and not have it.

an ETA and a visa are two different things

Technically true, but for visitors from the USA, it's a distinction without a difference for the most part.

OP did not specify if it is a single ticket booking or separate tickets.

If the latter, he might have a problem getting on his origin flight in the US ( assuming US is the origin) as to that airline his destination is the UK. If he does not have an ETA he could be denied boarding.

As Simon pointed out (in the 1st response), OP needs to provide more details to get a useful answer.

I got one, just to have it. If I'm transiting through the UK and get "stuck" and have to leave the airport, it's one less thing to worry about.

Not happy to hear that the BA agent wanted to see a printout, since the confirming email says it's automatically "attached" to your passport and nothing further is needed. Oh well, more belts and suspenders I guess.

Simon, sorry for not having the right wording. I had a major four-hour surgery this week so my head is still in a fog. As I was recovering I was thinking of my lovely international trip and Final Four Trip with my UCLA WMBB, both I took to get my mind off my 6th surgery in 2.5 years. I do try to be precise when I post but it was tough this past seven days.

Ditto what Frank II stated.

Soon I am traveling to Spain and because I’m transiting at Gatwick, not Heathrow or Manchester, I needed an ETA even though it’s one ticket.