The Lords Public Services Committee said that inequality would grow if money for the NHS, schools and councils was not protected.
This follows Government pledges to invest in "every part of the UK", with ministers promising a white paper published later this year to set out "bold new policy interventions".
The committee said the white paper needed to be released urgently to avoid the suggestion money is being channelled into Conservative seats.
The report added: "Without full transparency and political accountability, local areas will continue to question why they have missed out on 'levelling up' funding while others have benefited."
The plan involves investing in transport, skills and businesses in multiple places, from cities to rural and coastal areas, to address regional disparities in the UK.
The committee pointed to accusations the Government had favoured "prosperous rural areas with funds ahead of deprived communities", and said its strategy "does not recognise high levels of deprivation in many parts of the country, including parts of London".
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