Woolvershill, Hewish, Kingston Seymour and Brockley are next in line to enjoy access to the full-fibre network.
The broadband provider Gigaclear has started to carry out surveys in those villages.
Construction is expected to begin in early January, with the first people and businesses connected by the end of spring.
The engineering work is being done as part of the £171million Connecting Devon and Somerset programme.
It is the biggest publicly-funded broadband project in England.
Around 6,500 homes will be able to access better broadband once the latest round of work is complete.
More than 28,000 homes and businesses in North Somerset and Bath and North East Somerset have access to superfast broadband.