Any bingo site licensed in the UK will display its gambling licence number at the bottom of its home page. A UK Gambling Commission licence number is usually formatted 000-012345-N-987654-001.
You can use the Gambling Commission's Public Register to search for a bingo site, however, bear in mind that most bingo sites are licensed by a third-party software provider and therefore, the licensee name displayed will usually differ from the brand name.
For example, when searching for Wink Bingo, the results will show 888 UK Limited because Wink Bingo is powered by Dragonfish and is licensed by its parent company, 888.