The Home Office uses private companies to provide detention facilities for immigration purposes, as well for the provision of escorting and travel services in relation to Removals.
The operating costs for each of these contracts is commercially confidential and public disclosure would prejudice the commercial interests of the Home Office and its suppliers. However, the Home Office publishes payments in excess of £25K on its website at: https://www.gov.uk/government/collections/home-office-spending
The data available on the link above covers the period up to the end of January 2017. Further transparency spend data will be uploaded to this web address by July 2018.