Branches in Driffield and Pocklington will also close down, on June 4 and May 21 respectively.
A spokesman said: "We provide our customers with more ways to bank than ever before – customers can choose from a range of digital, face-to-face and local options.
"The way people bank with us has changed radically over the last few years: since 2014, the number of customers using our branches across the UK has fallen by 40%.
"During the same period mobile transactions have increased by 73%; and in the first half of 2017, there were 1.1 billion mobile and online transactions carried out by our customers: an increase 41% since 2014.
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"Since 2012 we have seen the way in which people use NatWest branches change dramatically."
· 88% of customers are already banking in other ways locally
· Transactions in NatWest Whitby branch have reduced by 38% since 2012 with now only 74 customers visiting the branch on a weekly basis
· 59% of customers are now choosing to bank digitally with us on a regular basis instead
The spokesman added: "We are communicating with our customers affected by the closure and proactively contacting vulnerable customers and regular branch users.
"We have extended the time between announcing our decision and the branch closure to six months; this has been done so that we can ensure our customers have enough time to consider the right banking options for them and to give us time to support them one-to-one during the transition.
"We know that not all of our customers are comfortable or familiar with using online or mobile banking, so we have created a new specialist taskforce of NatWest TechXperts who will be dedicated to supporting our customers with training and support with digital skills until the branch closes.
"We are following the Access to Banking Standard and we have made our decision after careful consideration of a wide range of factors including changes in customer usage of the branch over a long period of time; how often customers are using the branch and the types of transactions they undertake; the number of customers who only bank via the branch; and the other ways our customers can bank locally.
"We provide a range of alternative ways to bank, tailored to the needs of our customers and reflective of the way they live their lives. These include:
· Online and mobile: we are committed to educating customers on how to use these channels securely and simply.
· Telephony: our customers can contact us over the phone, via web-chat and social media. Our contact centres are open 24/7 and teams are trained to answer almost every query at first point of contact. Services available over the phone range from transfers and payments to opening new accounts, financial reviews and support with using digital banking.
· Video Banking: Customers are able to connect to our Video Bankers, wherever they are. They can assist our customers in many different ways, in a location chosen by them. These include full Financial Health Checks, opening personal accounts and discussing their short-term borrowing needs. This service can be accessed on a mobile or tablet, via a video connection.
· ATMs: There are a number of free to use cash machines in your area. Details of these can be found at link.co.uk/atm-locator, by calling 03457 888 444 or speaking to a member of staff.
· TechXpert: Our experts will offer training and support with digital skills; they will serve the branch until it closes and work in addition to our branch staff
In Whitby specifically:
· Post Office: We have a national agreement with the Post Office to provide our customers with a range of banking services. Customers can pay money in, take money out, check balances and business customers can get coinage. The closest Post Office is Bridge Street, 0.08 miles away from the branch; there are 3 Post Offices within 3 miles of the branch.
· Community Banker: Serving in the community and surrounding areas after the branch closure, Community Bankers will provide our customers with personal assistance in accessing the right banking options for their needs, as well as help with achieving their financial plans and goals. They will be able to work flexibly to support customers, including holding customer appointments in community locations and at customer homes where necessary.
· Other branches: The nearest branch, Scarborough, is 19.7 miles away