Many of the 110 residents, including Doreen Sheppard, 74, have complained of headaches and other health problems.
She said: "The masts are bound to be doing something. I get terrible headaches and I've started suffering from Meniere's disease, where I lose my balance. I'm worried about the children on the estate as there are so many of them now."
Both masts were erected in 1994. South Gloucestershire Council served a notice asking for them to be removed when the ten-year contract expired three years ago.
But because current guidelines say there is no risk from radiation the council does not have a legal right to force their removal.
After a long legal battle Orange has submitted a planning application to put the mast on top of a shopping precinct in a street near homes, a primary school and a public library.
Jeanette McCormack, 69, who has led a campaign against the mast, said a petition against the new location had gathered more than 200 names.
She added: "People of all ages who live and work near the mast will be exposed to the radiation and so there's a lot of anger about it."
World Health Organization guidelines have dismissed the risks of masts despite other evidence which has found they are harmful.
A spokesman for Orange said the company takes health and safety very seriously.
He added that the company was satisfied its mobile phone base stations do not present a health risk.
Vodafone is working on a new long term lease from South Gloucestershire Council. A spokesman said the company took residents' concerns "extremely seriously" and would continue to work with them and the council to provide reassurance.
Source-Medindia
GPL/J