Flying from Barcelona

Since you have a layover in London, the trip is not considered to be international. Therefore you only need to be there 2 hours ahead of time. So I would plan on getting there no later than 5:30 am. If you get there earlier, you stand a good chance of the check-in counter not being open yet (and I speak from experience).

That'll depend. On what exact day will you be flying?

The UK is not part of the Schengen Zone and not in the EU, so your flight to London is an international flight for which you would need to go thru passport control and security.
How far in advance you should be at the airport depends on what day of the week you’re traveling and what time of year. People can help you better if you share that information.

It's an international flight, so three hours would be recommended, but it's quite possible that a 4:30 arrival would have you looking at a lot of empty check-in stations (as I found in Madrid in similar circumstances). Google Maps shows several hotels close to the airport, which is where I'd spend that last night instead of in the city. For me, "stress free" means staying at the airport before an early morning flight, regardless of what city.

The UK is not part of the Schengen Zone and not in the EU, so your flight to London is an international flight for which you would need to go thru passport control and security.

That may be true, but last year when I flew from Glasgow to AMS, I was told to be there 2 hours early. I got there about 15 minutes earlier and had to wait for the staff to arrive before I could go through security. That said, London may be different.

Mardee; I think you may have misread the question. The OP isn’t asking about London. They have posted on the forum of Spain and want to know how early to arrive at Barcelona Airport for their flight to London.
The flight from Barcelona to London is an international flight for which they need to go thru passport control at Barcelona to exit the Schengen zone in addition to security.
You can’t compare this to a flight from the UK which doesn’t have the concept of exit passport control when you fly out of the country.

Three (3) hours is recommended by the Barcelona Airport’s website. Barcelona is an extremely popular destination with only one airport. If you hit the airport at a busy time for departing international flights, you’ll be glad you gave yourself three hours to run the gauntlet.
Have a great trip!

As far back as 2016 I needed every minute of the 3+ hours I had allowed at Barcelona when departing for the US. The hang-up for me was an unusually long line at the United counter.

Like many here, I'm a million mile plus flyer. I have never missed a flight due to not making it to an airport early enough. Unless a local tells me to be there 3 hours early or I plan on hanging out at an airport club, I never get there 3 hours early for a morning flight any longer. Showing up at 4:30 AM my experience has been you end up waiting for security or ticketing or something to open.

So if the local hotel tells you to get there at 4:30, then of course do so. But I'm in Mardee's camp on this one though. (Though there is nothing wrong with being careful.)