SVFR
You are correct that TBI are paying for ATCO 2s to provide the Luton Approach function from Terminal Control but that isn't the whole story.
When NATS were awarded the contract there were approximately 25 valid approach controllers at the in-house unit but only 14 of these were transfered as ATCO 2s to TC, the remainder stayed in the tower under various contracts. The Luton Approach function is now provided at TC by 12 of the 14 who transfered, two are currently unavailable due to sickness, plus about 12 ATCO 2s who were already at TC, already valid on Essex Radar or Gatwick and already paid by Area Services. Of the 12 Luton originals who transfered, 3 are now valid on Essex Radar or Gatwick.
I'm not sure how the funding of the approach services provided by TC works but you could argue that:
TBI are having the Approach Service for Luton subsidised by the BAA, who presumably pay for the Essex Radar and Gatwick radar function and the staff who provide it;
and/or
TBI are subsidising the Essex Radar and Gatwick Radar functions because staff that they pay for under the contract with NATS are also providing a service to BAA airports.
If and when Thames and SVFR arrive at TC it probably won't be too long before those services are also partly provided by ATCOs
who are currently valid on one or more of the existing approach units at TC.