The London site is is The Cube Bar on Finchley Road, which the company bought from the Mean Fiddler. Fitting out has just started and it should open at the end of May.
It has a 1am licence and a capacity of 230.
The second site, on Park Street in Bristol, previously traded as Tequila Worm. It will open in July.
It has a 2am licence and a capacity of 150. Both sites will be designed by Paul Daly.
Negotiations are "ongoing" for another two sites which the company expects to open within the next 12 months, according to Justin Carter, The Elbow Room's managing director.