Millions of pounds invested in troubled Icelandic banks by local authorities in Sussex and Surrey will not affect frontline services, councils have said.
Surrey County Council confirmed it had previously tried to withdraw its £20m investments in two Icelandic bank.
West Sussex council said it had £12.9m in Heritable, the UK arm of Landsbanki.
Gordon Brown said he was considering "further action", but the government is not offering to guarantee authorities' deposits with Icelandic banks.
The Local Government Association (LGA) had asked the government for protection for local authority investments.
West Sussex County Council said the £12.9m deposited in Heritable made up about 5% of its total funds in the banking system.
A spokesman said: "Unlike many local authorities, the county council has no investments directly with Landsbanki, so all of its money is held with UK-based banks.
"While the turmoil in the financial markets is of considerable concern, with a revenue budget of more than £1bn, this sum of money does not impact upon the day-to-day business of the county council."
Surrey County Council said its investments of £10m in Glitnir and £10m in Landsbanki would not affect frontline services because the council had "sufficient funds".
Michael Gosling, the council's executive member for resources, said the banks had had "long-term credit ratings of high, excellent or exceptional and met strict lending criteria" at the time of investment .
He said: "We attempted to remove our investment prior to the current situation, however as we were tied into a deposit period of up to two years, we were unable to do so."
Lewes council had £1m invested in the Icelandic bank. The council said services would not suffer.
Brighton council said it had withdrawn deposits from Icelandic banks.
A spokesperson for the council said it suspended transactions with Kaupthing Singer and Friedlander about a year ago over concerns about Iceland's banks expanding too rapidly.
Deposits from more than 100 councils across England, Wales and Scotland could be at risk, the BBC has learned.