Local councillors have joined customers in condemning the move which, they say, significantly weakens facilities in both villages.
A caller to the Review said the Newnham branch closure was a serious blow to many pensioners.
"Not all of us have cars. We conducted our business through Lloyds Bank and this will make life very difficult for us. We will now have to rely on a member of the family to take us to Lydney or Cinderford," she said.
Lloyds say they take no pleasure from the decision to close the branches but in both cases customer numbers had fallen in recent years.
Senior branch manager Mark Hartery said:"The number of customers using Bream and Newnham has been falling for some time and we can no longer justify keeping these branches open when our future in the Forest of Dean clearly points to the larger towns."
Mr Hartery said Lloyds TSB had backed an initiative to introduce banking services in post offices in rural areas where it was not possible to sustain a branch.
"Money can be paid into and withdrawn from one's account at post offices which has been a great help to people who live in rural communities," he said.
The Bream branch closes on April 12 and Newnham on April 20. Newnham staff Trudy Middleton and Glenda Yarworth will work from Lydney while Bream's Glenda Oliver is looking to retire early.