In March 2008 HMRC published details of analysis from 2005 that attempted to derive broad-brush estimates of the direct tax gap at the start of the decade. This publication contained a net tax gap estimate for stamp duty land tax of £0.5 billion, within a range of £0.2 billion to £1 billion and can be found at:
http://www.hmrc.gov.uk/research/direct-tax-gaps.pdf
and
http://www.hmrc.gov.uk/research/measuring-tax-gap.pdf
The most up-to-date information is found in “Measuring Tax Gaps 2009”, published at PBR 2009, which contains an illustrative indicator of the tax gap for all stamp duties, available at:
http://www.hmrc.gov.uk/stats/measuring-tax-gaps.pdf