The independent reviewer has also challenged the new two-year-limit on TPims - a restriction that wasn't part of the previous control order regime scrapped at the start of 2012.
For Labour, shadow home secretary Yvette Cooper said it was clear that the security services and police were concerned about the operation of TPims and the possible impact on UK security.
He added the end of relocation powers had been balanced by increased resources for surveillance, and TPims were limited to two years as opposed to the indefinite length of control orders.
In March, the independent reviewer of terror laws, David Anderson, said TPims could prove less effective than control orders because they can be imposed for a maximum period of two years only.
The names of most of the men who are subject to TPims have not been made public - but Mr Anderson said the Home Office should supply "information regarding the location of T-Pim subjects" on a region-by-region basis.