The move - which will put 2,000 jobs at risk across the country - is part of a wider plan to transform Sainsbury's eat-in, takeaway and home delivery food and drink offering.
The closures will be as soon as April.
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In its place, Sainsbury's - in partnership with Boparan Restaurant Group - plans to open 30 restaurant hubs after a successful trial in Birmingham.
There, customers will be offered eat-in, takeaway and home delivered hot food and drink from brands including Caffè Carluccio’s, Gourmet Burger Kitchen, Ed’s Diner and Slim Chickens.
It's not known whether Bedford's Clapham Road store will get a Starbucks coffee shops at this stage.
Simon Roberts, Sainsbury’s chief executive officer, said: "“As we go through this period of transition, we have taken the difficult decision to close 200 of our cafes next month.
"We have spoken to all colleagues affected by these changes today and are absolutely committed to supporting them in any way we can during this uncertain time.
"Of course, we understand this is very unsettling for our colleagues, but we must keep adapting our business to make sure we are offering customers the best possible food and drink at affordable prices.”