Council chiefs have set aside the sum as part of moves to get to the bottom of claims that child-sex gangs were operating in the town for decades.
Last week an extraordinary meeting of Telford & Wrekin Council gave the green light for an independent public inquiry following claims in a national newspaper that up to 1,000 girls may have been abused over a period of 40 years.
Under the move Councillor Lee Carter is now the cabinet member with special responsibility for the inquiry, and an initial advisory group made up of two representatives from each political group will be set up to arrange the scope of the inquiry and recommend a suitable inquiry chairperson.
A new cabinet report states: "The council’s Service & Financial Planning Strategy includes a clear priority to protect those most vulnerable in our society and will use its resources as effectively as possible to deliver the best possible outcomes for the community. The 2018/19 strategy includes a capacity fund which will be used to fund the approved recommendations in the 29 March cabinet report, including a co-ordinator post, additional capacity for the Children Abused Through Exploitation Team, support from the voluntary sector and commissioning the charity National Working Group to carry out a health check.
"Telford & Wrekin Clinical Commissioning Group and West Mercia Police and Crime Commissioner have both agreed to contribute £70,000 to support the initiatives outlined. Further, the Local Government Authority have confirmed a contribution to the National Working Group Health Check on the grounds that any learning will be shared nationally.
"It is very difficult to estimate the costs of running a Local Inquiry however £0.350m will initially be set aside in a reserve from the projected 2017/18 underspend.
"The council has the authority and discretion to commission an inquiry into its own activities. The inquiry will need to discuss the proposed investigation with other organisations involved before it begins, to establish primacy of other inquiries for example ongoing criminal investigations or statutory inquiries to establish co-operation and to avoid duplication.
"The inquiry could forseeably be looking back to before when Telford & Wrekin Council was created in 1998. For that period, and with the exception of current employees, it will largely rely upon the co-operation of organisations and individuals and has no authority to compel the production of documents or the attendance of witnesses for interview."
Telford & Wrekin has been responsible for social services and child welfare since 1998. Before that, responsibility fell to the former Shropshire County Council.
The national Independent Inquiry into Child Sexual Abuse is also bringing its Truth Project to the borough next month to hear from victims.
Seven Telford men were jailed in 2013 following the police Operation Chalice investigation on child sex abuse charges which led to an Independent Review.