Five branches in London will be closed by April next year, with two, in Archway and Stamford Hill, to be refurbished by March 2017.
The bank said that “less well used” branches will be closed, arguing that in many locations customers were choosing one out of two branches in close proximity.
Prior to today's announcement, the bank had closed a total of 30 branches since the start of 2015.
TSB launched in 2013 with 631 branches, and does not expect the closures to alter the proportionate size of its network, at roughly 6 per cent of the UK's total branches.
The change programme will see the Sabadell-owned challenger bank modernise around 100 branches in total, while also opening new flagship branches, beginning in Birmingham and Aberdeen, both of which are set to open their doors before the end of 2016.
As a result of customer feedback, the new branches will have more self-service machines as well as tablet computers for logging into internet banking services, and large interactive TV screens, while also featuring boosted areas for face-to-face customer interaction.
Following a deal with unions Unite and Accord, the bank said that there will be no compulsory redundancies, with TSB staff, which it calls partners, given the choice of relocating to new branches within 10 miles.
Accord general secretary, Ged Nichols, said: “We understand the desire to improve the inherited branch network to make them better places for customers and partners. But, it’s really important these changes are managed in a sensitive and respectful way for impacted people. It’s also important that partner’s contractual positions, employment rights and union agreements are fully observed.”
A Unite spokesman declined to comment.
TSB distribution director Peter Navin said: "We've made a commitment to our customers to keep delivering the type of banking they want and deserve; a key part of that is having the right branches in the right places."