Services in Ellesmere and Albrighton are among the first 18 being launched in April, with the others to follow between now and the summer.
They will allow customers to make payments, get help with products and services, and assist with bereavements.
Following branch closures announced last year, TSB said it has engaged with communities, customers, staff and politicians to ensure its face-to-face banking services are suited to the evolving habits of customers and the needs of communities.
The 43 pop-ups are spread across the UK, with 22 in England, 19 in Scotland and two in Wales.
The majority are based in locations where it takes TSB customers longer than 20 minutes to travel to their nearest branch. TSB has introduced 100 mobile adviser roles to deliver the new face-to face service, which will offer customers end-to-end access to products and services outside of a branch.
Locations for the pop-ups include popular locations already used by members of the local community for other services, like town halls, libraries or community centres.
In addition, TSB is also finalising a small pilot to explore new ways for customers to access cash.
This pilot, which is due to get underway next month, will allow these customers to use a digital platform to deposit cash in some local shops or supermarkets. TSB is partnering with global payments and financial technology company Diebold Nixdorf and specialised payments platform Paysafe to pilot the concept in communities in Glasgow, Newcastle, Manchester, Liverpool and Birmingham.
TSB is also one of the banks participating in the Community Access to Cash Pilots (CACP), in Denny, Cambuslang and Hay-on-Wye, which are co-ordinated by UK Finance and Natalie Ceeney.
Carol Anderson, director of branch banking, said: “Although we’ve seen a significant rise in customers using digital banking, we know accessing banking services and cash remains important to many customers and we’re always looking for innovative and inclusive ways to help them.
“The pop-up service will support our customers in parts of the country where it takes longer to get to a branch. The pop-ups and future access to cash pilot will test demand for these types of services, giving us insight on what more we can do for customers in the future.”