The new build will be Whitbreads largest London opening for this current financial year, and will compromise the groups Bar and Block steakhouse concept.
It will be joining existing Premier Inn hotels in the area, which includes the Premier Inn London Southwark, situated on Borough High Street and Bankside-based Premier Inn London Southwark.
The hotel will also include a public courtyard and park.
Alex Flach, UK development director at Whitbread, said: “While the coronavirus pandemic has created significant challenges for the hospitality industry, we remain committed to our strategy of growing and innovating Premier Inn and hub by Premier Inn in the UK and Ireland.
“Reaching practical completion of new Premier Inn hotels in Milton Keynes and on The Cut in Southwark takes us a step closer to adding 450 new Premier Inn rooms in the prime locations our customers want to be.”
Flach added: “The hotels and restaurants are in the heart of the action, look fantastic and we’re confident they will be very popular with our customers when they open later this year.”
The news comes as Whitbread has announced it is reopening construction sites in Edinburgh, Glasgow, Hamilton and Thurso as it looks to “safely” continue its plan to deliver a pipeline of new hotels in Scotland.
The sites in question account for £55m of investment by the Premier Inn owner and its development partners.
Work will now resume on a new “super-sized” 249-bedroom hotel in Glasgow’s St Enoch Square, a 136-bed hotel on Edinburgh’s Princes Street and a site in Thurso in the Scottish Highlands.