Low cost air carrier from London to Continent

I use skyscanner.com to reseach intra-European flights. Though I have been successful so far in avoiding RyanAir, others (especially those traveling with small carry-on bags) are OK with it. There are quite a lot of other options, depending on the places you might like to travel to: Vueling, Wizzair, and so on.

You can find a list of all destinations served from Heathrow or Gatwick, by airline, on each airport's Wikipedia page. However, those lists are likely to be so long as to be not very helpful.

In 2019, we flew from/to London to:from Marrakech on East/Jet. Didn’t feel welcome on tge flights, especially the return, but it got us there, for an acceptable price.

I wasn’t exactly taking note of all the options, but it seems our only alternatives at the tone were bc Ryanair and Royal Air Maroc.

Is Spain a consideration? Is Vueling still flying? What about Norwegian - is that any possibility?

If you abide by the airline’s baggage policy, then Ryanair are fine. They have always got me to my destination on time. EasyJet are my preferred airline.

Wizzair have a dreadful reputation in the U.K.- several friends have vowed never to use them again after cancelled flights and delays.

Be careful with a non-linked flight, as any delays to your incoming flight may cost you dearly.

Tui also fly to Marrakech from Gatwick

It may be helpful to expand Jennifer's comments. "Linked" flights are also known as self-transfer. What it means (usually) is that the second flight is like starting over, checking in your luggage and presenting your ticket in the lobby. It's not a connection in the traditional sense. Miss the scheduled flight; buy another ticket with no refund. With so many companies, there may be exceptions. And the traditional airlines have adopted some of the budget strategies, within Europe, to stay competitive.

Easyjet, Ryanair, I can recommend, but there are dozens: https://en.wikipedia.org/wiki/List_of_low-cost_airlines#Europe

I don't understand the hate that Ryanair gets. I've flown Easyjet, Vueling, Norwegian, Tui and several defunct airlines like BMI and Flybe. Ryanair is really no worse than any of them - just make sure you read and fully understand the T&Cs. The important part of the description is "Low Cost" - you seriously cannot expect flag carrier service at , often, a quarter of the price.

I've never flown Ryanair and never will, the moron that runs the airline is enough to put me off. Never understood how people can pay money to someone that thinks all his customers are stupid.

Note that some bargain airlines use less convenient secondary airports.

Whilst i am no fan of O'Leary that doesn't stop me using Ryanair
Had some good bargains over the years such as to Norway for £9.99 each way

To my knowledge RyanAir is the only airline that requires US citizens to go through a separate passport check, usually at a completely different (and reportedly sometimes hidden) desk before completing check-in.

Some other fees are also much higher than those charged by EasyJet (just one example, and I'm not suggesting EasyJet is a paragon of passenger-friendliness):

Name change on ticket: RyanAir €/£115 online, €/£160 by agent. EasyJet $65 online, $75 by agent; free to correct spelling mistake or change title.

Airport check-in: RyanAir €/£55. EasyJet lists no such fee, which I assume means you can check-in at the airport at no extra cost.

Boarding card re-issue: RyanAir €/£20. EasyJet lists no such fee, which I assume means you can get your boarding pass reprinted at no extra cost. (I once needed to do that when traveling on a legacy airline; I somehow dropped the boarding pass between the check-in desk and the gate.)

The large print giveth, the small print taketh away

Acraven
Most of the things you have listed the normal traveller shouldn't need to do.
What they have done over the years is to tighten the free baggage allowance and reduce the time period before flights when you can print your boarding card.
You can of course alleviate these by paying extra.

I flew RyanAir from Stansted London to Santorini and it was a breeze. As US Citizens traveling on US passports, we went through the same lines everyone else did. We didn't fly them because they were low cost but because they had the most convenient flight times to Santorini.

Coming back from Mykonos to London June 5th, WizzAir canceled our 5AM flight at 4AM leaving 250 people stranded with no refunds, no hotels, nothing.

This happened June 5th. After weeks of no contact whatsoever from Wizz Air, I refuted the charges with my credit card and won on September 1st.

Wizz Air has zero customer service.