They are very afraid, euro soccer governing body EUFA and FIFA have set up task force to monitor odds movement for suspicious activities, for example. All the big bookmakers, street and online, are signed up to cooperate. Most of the evidence from the big Singaporean match fixer that recently got caught started out of these investigations. UEFA doesn't allow betting ads in the Champions League and Europa League.
In terms of the exposure to betting, countries have 3 stands. Those that view it as a people's right such as the UK and Sweden, the people's money the people can do whatever they want. Those that restrict to protect local monopolies like Netherlands at the country level and some German States as the provincial level. And the clueless ducks like Spain (up until last year where they pass some legislation) where people and companies didn't have to comply with anything because there was no mention of it in any law.
But ultimately the European Union has pronounced in favor of open betting, so even if a Swedish bookmaker is booking dutch citizens and breaking Netherlands laws they don't get arrested and prosecuted like in the US because no EU law is broken. They can bitch and moan all they want but can't do anything about it unless the bookmakers want to cooperate. One way they are making the bookmakers cooperate is by restricting advertisements and exposure in the media, billboards etc, those things that they can control at the local level. And really it's such profitable racket that it's in the bookmaker's best interest to just cooperate even if you get hit with a tax or license or whatever.
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