The news came after the Downham branch of Norwich & Peterborough (N&P) building society closed its doors for good on Friday, following an announcement by parent company the Yorkshire Building Society (YBS) earlier in the year. In England and Wales the number of NatWest branches will fall to 655.
RBS planning to close a quarter of its branches and shedding 680 jobs, due to an increasing number of customers opting to use online banking out of convenience as opposed to visiting high street branches.
The bank said it was seeking to manage job losses on a voluntary basis and keep compulsory redundancies to a minimum.
Since 2014 the number of customers using our branches across the United Kingdom has fallen by 40% and mobile transactions have increased by 73% over the same period.
"Given the distances that will now be involved in finding the nearest RBS branch, I imagine many customers will be seriously considering moving their accounts because other banks are, after all, available".
He said: "While we appreciate that many customers are choosing to access services digitally, and there clearly has been rapid growth of online banking at RBS in particular, there are many customers for whom this is neither a practical option, nor an option they are comfortable with, perhaps where they may be more fearful of online fraud".
The union's national officer Rob MacGregor also said that the move could effectively signal the end of banking in branches.
"This announcement will forever change the face of banking in this country resulting in over a thousand staff losing their jobs and hundreds of high streets without any banking facilities".
In March, RBS announced that it would close 158 branches in the United Kingdom, as more customers switch to digital banking.
But the trend has prompted fears for communities being left without a bank in their town and those unfamiliar with the developments of the digital age being cut adrift.
Mr Wheelhouse wants the support of the United Kingdom government in calling a halt to Royal Bank closures - and any others planned by other banks - while both Scottish and United Kingdom governments thrash out a plan that will "take account of its obligation to its customers to provide a banking service that meets their needs".
On Thursday, RBS announced the closure of its so-called "bad bank" - the unit set up to dispose of large chunks of unwanted assets following its £45bn taxpayer rescue - marking another chapter in its recovery.