You would only have a license if you are taking bets yourself, which you're not - there's no requirement for affiliates to be licensed and you wouldn't get a license (assuming you are acting as an affiliate rather than providing software to any operators etc). You should tell them that you are an aggregator or sports focused site rather than accepting any bets yourselves, and are only promoting UK licensed operators (if you are advertising to UK based consumers, it is illegal to advertise non UK licensed operators). The advertising sources may want you to prove that the operators you are advertising are whitelisted though, which would be more difficult.
From a quick glance at your site I don't believe
BetButler are UK licensed any more.