I have not been able to find more details on those specific cases but some info on the asylum process may perhaps begin to shed some light on the issue:
- An application is just that, nothing more. People can claim they are persecuted even when they aren't. Ideally, a country should be able to process applications quickly and reject ludicrous ones even quicker but everybody can apply for asylum and in practice it does take many months for officials to come around interviewing asylum seekers and reaching a decision (it's not easy either, you need people familiar with the law and the situation in the country of origin of the asylum seekers, translators, etc. to conduct those interviews).
- It certainly makes for good tabloid material because Spain feels like a particularly harmless country and it's in the European Union so closely associated with the UK but applications from citizens of presumably safe countries like the US and Canada are nothing new and probably unavoidable. The standard to be met is that you must personally face persecution and can't count on the protection of your country of origin, not necessarily that you come from a failed state or a place at war.
- That's even rarer than unsuccessful applications but there is no need to come from a place with widespread persecution to successfully claim asylum. Cases in point: Christoph Meili, a Swiss citizen granted asylum in the US or Denise Harvey, a US citizen granted asylum in Canada. Applications from US or Spanish citizens are exceedingly unlikely to succeed but they are not going to be summarily dismissed based only on the citizenship of the person (or at least that's the case in the UK and many other countries and in international law but the German concept of sicherer Herkunftsstaat basically allows filtering by citizenship).
- Conversely, coming from a country where there is genuine widespread persecution or civil war is not enough in and of itself to be granted asylum. I have known some Algerian people who had great difficulties getting asylum during the civil war there (e.g. because of some aspect of their biography like having previously worked for the security forces). I also know many people from the DR Congo who apply for asylum but get turned down because they can't prove they come from the east of the country (which is the most unstable region).
Incidentally, that's the most puzzling thing about this story for me. If you come from Congo, you are faced with deportation and claiming asylum is your last option, then I completely get why you would try to make up a story to be able to stay, I would do it myself if I was stuck in this situation. But if you come from Spain you have many easier ways to remain in the UK perfectly legally… And even if you have to leave, coming back is also very easy, legally and practically.
One wild guess is that some of these asylum seekers are people who tried to come under free movement rules, find themselves out of a job and resources or in some sort of special difficulties and see that as a means to remain in Britain and claim some benefits that are otherwise not available to EU citizens (free movement rights are extensive but not absolute).
And adding the numbers for five years gives a stronger impression but we are only talking about 100 cases a year, give or take, so less than half a percent of all asylum applications and perhaps 0.1% of EU citizens migrating to the UK every year. Arguably, 0.5% of anything should not really be treated as news or be worthy of a cabinet minister's time.
More generally, it's a fact of life that a large country like the UK needs a system that can process tens of thousands of asylum applications a year (France or Germany get two or three times as many as the UK, without counting the current wave of people coming to Germany) and be robust to some number of ludicrous applications and other freak cases. And that does cost something, obviously as do the many applications from people who are genuinely in distress.