If I'm flying with BA intra-Europe (Stockholm-London), am I allowed to have my cats (in their cat-cage obv) in the cabin, under a seat or on my lap or something?
It appears not, according to the British Airways website:
Making your booking and taking your flight
The DEFRA Export Section (Dogs and Cats) will advise you of the current documentation and vaccination requirements for your destination. We will also require a health certificate from your vet to show that your pet is fit for air travel.
When you make your booking you will need to let your travel agent or British Airways booking representative know that you will be travelling with a pet.
Your pet will not be able to check in with you but will be handled professionally by British Airways World Cargo, a cargo booking will be required which can be requested through the local British Airways World Cargo booking office.
On the day of travel, deliver your pet to the British Airways World Cargo Office. The travel container will be checked and the appropriate charges collected. Please check local payment options when making your booking.
BA have a really good page about pets on their site
The bad news is that only guide dogs are allowed to be taken on the plane with you. All others must travel in the hold.