Monday and Tuesday bring early games thanks to double-headers, with the Yankees and Tigers playing a twin set on Monday and the White Sox and Twins doing likewise on Tuesday.
The early games on Wednesday include one from an intruiging interleague series between the Milwaukee Brewers and Cleveland Indians, whilst the Facebook exclusive game is D-Backs versus Giants.
Thursday and Friday offer Cubs fans the chance to watch their time at a convenient time both days, catching the final game of their home series against the Phillies on the former and the first game of their series against the Pirates on the latter.
All times are in BST.
Monday 4 June
18:10 Yankees at Tigers (Severino (8-1), TBD) *MLB.com Free Game, BT Sport/ESPN
Tuesday 5 June
21:10 White Sox at Twins (Lopez (1-4), TBD) *BT Sport/ESPN
Wednesday 6 June
18:05 Rays at Nationals (TBD, TBD)
18:10 Orioles at Mets (Bundy (3-7), Wheeler (2-4))
18:10 Brewers at Indians (Anderson (4-4), Carrasco (6-4))
20:40 Braves at Padres (Foltynewicz (5-3), TBD) *BT Sport/ESPN
20:45 D-backs at Giants (Buchholz (1-1), TBD) *Facebook Game
Thursday 7 June
17:35 Rockies at Reds (Anderson (3-1), Harvey (1-4))
17:35 Dodgers at Pirates (TBD, Taillon (3-4)) *BT Sport/ESPN
18:10 White Sox at Twins (Shields (1-6), Berrios (6-5)) *MLB.com Free Game
18:15 Marlins at Cardinals (Hernandez (0-3), Mikolas (6-1))
19:20 Phillies at Cubs (Pivetta (4-4), Chatwood (3-4))
Friday 8 June
19:20 Pirates at Cubs (TBD, Montgomery (1-1)) *BT Sport/ESPN.
All of these games are available to watch or listen to live via an MLB.TV subscription, other than the Facebook live game which is exclusive (but free) to Facebook subscribers. TV coverage of MLB in the UK comes courtesy of the BT Sport channels and these are highlighted above, as are any games that are available to view online for free via MLB.com. The above list of games just shows those starting before midnight UK time. The full schedule of MLB games can be found on MLB.com