I’m not incredibly knowledgeable about the Casino industry as of yet, but I would assume that visitors would feel more comfortable in signing up to Casinos/companies that they are familiar with.
Seeing as I’m from the UK, the names that I would immediately recognize are:
Ladbrokes
Bet365
Betfair
William Hill
Then there is also 32red, which seems pretty focused on attracting the UK crowd, with currencies being displayed in GBP rather than EUR or USD.