Up to 200 footballers may have been affected, with some losing their homes and being made bankrupt.
“This was not a case of greed or bad decisions,” said the cross-party parliamentarians.
“These men did what we ask of everyone – they saved for their futures, trusted regulated professionals and followed advice they believed was sound.
“We believe that these victims have been failed by not only their advisers but also the financial services sector, by regulatory and law enforcement bodies, by HMRC, and by the football industry.”
City of London Police opened an investigation in 2018.
Two years later it was closed, with the force concluding there was “insufficient evidence to support a realistic prospect of conviction”.
No charges were brought against Kingsbridge staff.
Lord Mann, Sobel and Bool have called for “a thorough investigation into the conduct of all advisers and schemes involved” and “a fair and timely resolution to the decade-long tax dispute”.
Bool said she wants “to see a leniency package put in place by HMRC” for the V11 group.
In a statement HMRC said: “We have a duty to collect tax when it is legally due.
“We recognise that dealing with an enquiry and a large tax liability can be stressful and we are absolutely committed to identifying and supporting customers who need extra help.”