My concern is that there's a chance that my travel companions will be detained if the person at the border doesn't believe that they want to come on holiday. They might suspect that I'm trying to smuggle two EU citizens into the UK under the guise of a holiday.
I don't want to sound patronizing, but it seems like you need to take a deep breath. For every case you've seen of someone being detained, and for each of the thousands of cases you haven't seen, there are millions of cases of people being admitted to the UK, undertaking their planned visits, and leaving, with no incident whatsoever.
Yes, the immigration officer might suspect that you're trying to smuggle them in, but it's extremely unlikely. The cases you've read about mostly involved people who really were planning to do something forbidden by UK immigration law, even though many of them did not realize it. Others were detained incorrectly because of widespread misunderstanding among Home Office staff about permissible activities for visitors (that is, it's allowed for visitors to look for work, but many immigration officers seem to think that it is not). But you're not proposing anything that might be seen as impermissible, much less anything that is actually impermissible.
Maybe you won't speak to an immigration officer at all, since as far as I know, EU citizens can still use the automatic passport gates (as citizens of several non-EU countries have been able to do for some years now).
My question is will it help or hinder if we approach the passport desk as a group?
My guess is that it will help. But if you're really worried about this, the trick is to be prepared for a challenge just as anyone should be, whether a citizen of Spain or Japan or Nigeria.
If you live in Spain or have other ties there, you should be prepared to show evidence of that, too, because it tends to reduce the probability that your girlfriend would want to remain in the UK to be with you.
If you are questioned by an immigration officer, don't show anything unless you have a reason to. You don't want them to be suspicious that you're too well prepared, which might cause them to think that you have something to hide. Just be prepared to address concerns that the officers might have if the officers show signs of actually being concerned.
Don't bring a large amount of luggage. The first person I ever heard of who was turned away at the border was an American who was in fact planning to overstay in the UK. She had brought a huge suitcase for a visit that was supposed to be two weeks.
Or should they approach the desk separately from me?
If they can use the automated gates, of course you should all do that. If they cannot, then everyone will be a lot less nervous if you all go through the line together and present yourselves together. If one of you is flagged to speak with an officer, you should go together to keep your traveling group intact. If they really want only one of you, they'll let you know.
Or should I give up on the idea of going to UK with them?
Absolutely not.
