Easy Jet flight Amsterdam to Malaga with a change in London in the middle. Not allowed to board flight because of no UK entry Visa

You may have fallen between the cracks here.

You have booked two seperate tickets and hence you would need a "Visitor in Transit" visa and not the "Direct Airside Visa" you have linked. In either case though, you should be exempted as a holder of an EEA residence permit. See https://www.gov.uk/check-uk-visa/y/india/transit/somewhere_else/yes

However, most airlines use IATA to check entry requirements and if you poke in your data (as single flight from AMS to the UK), you would indeed need a Visa to enter into the UK. See https://www.iatatravelcentre.com/passport-visa-health-travel-document-requirements.htm

It depends here how the agent entered your information into the IATA search system. If they would have entered it as a single trip with a layover in the UK and a dutch residence permit you would be fine without a Visa.

Since Easy Jet is "point to point" airlines which doesn't allow booking connecting flights, the agents probably entered this as a single AMS->LON trip.
This makes sense since the UK concept if "Visitor in Transit Visa" is fairly unique, for almost all other countries there is no difference between "connecting on separate tickets" and "entry into the country". IATA has no concept of "transiting on separate tickets"

What can I do about this situation?

Read up on Easy Jet's terms and conditions. Look for "denied boarding" and check what the rules and potential compensations are. Contact Easy Jet with documentation that your status was "Visitor in Transit" since you had an onward ticket in less than 48 hours and that you were exempted from a Visa requirement because of your EAA residence permit.

There are two points here:

1. You selected "Airside Transit" in the link you gave, but you are flying with Easyjet, which means you would have two separate PNRs for the journey. That means the destination of your flight from Amsterdam is UK (not Malaga) and you should have authorization to enter UK. Even if you don't have checked in luggage and your actual intent is to make airside transit, that is not accepted by airlines unless you have a connecting flight (ticket till final destination on a single PNR). The visa required in such cases is "Visitor in Transit Visa" (not Direct Airside Transit), to be allowed boarding.

2. Even if you have to pass through border control, having a "common format residence permit from an EEA country or Switzerland" allows you to transit without a visa (TWV) but it is discretionary. Normally people are granted 48 hour leave to enter the UK to change planes or even airports. Therefore I have seen a lot of cases where airlines denied boarding even to holders of a non-UK visa which exempts a visitor in transit visa, but I have also seen cases where airlines allowed boarding to Indian citizens without any UK visa who even had to change airports in the UK and were granted temporary entry without a problem by border agents. But these cases were of those who were traveling to the US or Canada on a single PNR but had a change of airport (Heathrow to Gatwick).

The discretionary nature of the provision provides a lot of leverage to the airlines to make boarding judgements. Going to North America from India on a single PNR ticket and going from mainland Europe to mainland Europe, thus effectively taking a detour, via UK on two separate tickets are two very different cases.

But I have never personally known an airline allowing boarding to the UK (to Indian citizens) with different PNR tickets. You may try to contact EasyJet quoting the UKVI website (please also show them the page where you are even allowed to travel where you need to pass through passport control). But as the decision rests with the airline, and the language on the UKVI website makes the provision sound very discretionary so you may not a positive response from them.

The main point is that Easyjet do not sell connecting flights. So what you actually bought was a flight from Amsterdam to London, and, separately, a flight from London to Malaga. You did not buy a flight from Amsterdam to Malaga with a connection in London (Easyjet just don’t sell that).

To let you board the flight from Amsterdam to London, Easyjet would have needed evidence that you would be allowed entry into the UK, without taking into account any further flights booked with them or anybody else. You definitively didn’t qualify for that. For them, that’s the end of the story.

Some airlines and/or agents will take into account further flights (with the same airline or with another airline). But they hardly have any obligation to do so, quite the contrary. Anything that would make anyone consider that the flights are somehow connecting could open the door to a whole new collection of problems for them (if you miss your connection, and they become liable for care, assistance and possibly compensation). So they have every reason to completely ignore any further flights, even if they’re booked on the same airline.

I’m afraid that in your situation, if you want to travel between Schengen airports, either travel only via other Schengen airports, or make sure all flights are on the same ticket/booking/PNR and you can transit airside and match the conditions for that.