For Xbox One recommendations:
Lego games. There’s Lego marvel, Avengers, Star Wars, Jurassic World, Batman etc. All are great games, depends really on what kind of movies/stuff your kids are into. Can be played 2 player.
Minecraft is a must. Usually cheap (under £20) and is super huge open world game. Can be played 2 player.
Forza if they like racing, but there are different games depending on which type of racing they want. Forza motorsport is the original proper racing-on-tracks game with sports cars, with Forza 7 being the newest release. Forza Horizon (3 is the newest) is more off-road, open world racing, so dirt tracks and deserts and jungles etc.
If they like football, Fifa. If they like basketball, NBA. If they like hockey, NHL. If they like American football, Madden. 18 is the newest for all of these.
There are a lot of downloadable smaller ‘indie’ games too that are great fun, like Cuphead and Ori and the Blind Forest. These need to be bought as codes in a shop or on the Xbox store on the console (you’ll either need to add a credit/debit card or buy credit vouchers in a store to buy them on a console)