The following table lists bypass schemes which have been completed in each of the last 10 years by either the Highways Agency or the relevant local highway authorities.
Scheme 1999 Dudley Southern Bypass, West Midlands Coalfields Link Road Phase 1, Barnsley Leeds Inner Ring Road, Stage 6, Leeds A30/A35 Puddleton Bypass (DBFO) A564 Derby Southern Bypass Contract B 2000 A617 Rainworth Bypass, Nottinghamshire 2001 A174 Skelton and Brotton Bypass Burntwood Bypass Phase 1 and 2, Staffordshire A151 Weston Bypass , Lincolnshire C541 Addlethorpe Bypass and Bends Improvement, Lincolnshire 2002 A143 Broome-Ellingham, Essex A131 Great Leighs, Essex A6023 Denaby Main Diversion, Doncaster A511 Ashby Bypass Stage 2, Leicestershire A27 Polegate Bypass, East Sussex A43 Silverstone Bypass (A43 M40 to B4031 Dualling), Northamptonshire A43 Whitfield Turn to Brackley Hatch Improvement (A43 M40 to B4031 Dualling), Northamptonshire A6 Clapham Bypass, Bedfordshire A66 Stainburn and Great Clifton Bypass, Cumbria Wyre Piddle Bypass, Worcestershire A428 Crick Bypass, Northamptonshire (Developer Funded) 2003 A350 Semington-Melksham Diversion, Wilsthire Barnsley Coalfields Link Road (aka Shafton Bypass) A6 Great Glen Bypass, Leicestershire A53 Hodnett Bypass, Shropshire A5 Nesscliffe Bypass, Shropshire A500 Basford, Hough and Shavington Bypass, Cheshire A6 Rothwell-Desborough Bypass, Northamptonshire A6 Rushden and Higham Ferrers Bypass, Northamptonshire A6 Alvaston Bypass, Derbyshire A650 Bingley Relief Road, Yorkshire A4146 Stoke Hammond and Linslade Bypass (Northern Section), Buckinghamshire A41 Aston Clinton Bypass, Buckinghamshire A527 Biddulph Inner Bypass, Staffordshire Ashton-under-Lyne Northern Bypass Stage 1, Tameside 2004 St. Clements Way, Thurrock (aka West Thurrock Marshes Relief Road) A607 Rearsby Bypass, Leicestershire Mansfield Ashfield Regeneration Route, Nottinghamshire A63 Selby Bypass, North Yorkshire A10 Wadesmill to Colliers End Bypass, Hertfordshire 2005 A167 Chilton Bypass, Durham A21 Lamberhurst Bypass, Kent A47 Thorney Bypass, Norfolk A142 Fordham Bypass, Cambridgeshire Gloucester South West Bypass (Castlemeads section) A5 Weeford-Fazeley Improvement, Staffordshire A158 Coastal Access Improvement Phase 1—Partney Bypass, Lincolnshire A428 West Haddon Bypass, Northamptonshire (Developer Funded) A57 Cadishead Way (Brinell Drive to City Boundary), Salford Burntwood Bypass Phase 3, Staffordshire 2006 A505 Baldock Bypass, Hertfordshire South Lowestoft Relief Road, Suffolk A421 Great Barford Bypass, Bedfordshire 2007 Barford Bypass, Warwickshire A58 Blackbrook Diversion, St. Helens, Merseyside A197 Pegswood Bypass, Northumberland A1198 Papworth Everard Bypass, Cambridgeshire A612 Gedling Integrated Transport Scheme, Nottinghamshire A429 Barford Bypass, Warwickshire Barnstaple Western Bypass, Devon A38 Northfield Regeneration Relief Road, Birmingham Rugeley Eastern Bypass Stage 2, Staffordshire A4146 Stoke Hammond and Linslade Western Bypass, Buckinghamshire Cradley Heath Town Centre Relief Road, Sandwell Sheffield Northern Inner Relief Road, Sheffield A158/C541 Coastal Access Improvement Scheme, Phase 2—Burgh Le Marsh Bypass, Lincolnshire A165 Reighton Bypass, North Yorkshire Ridgmont Bypass and Woburn Link Road, Bedfordshire A66 Temple Sowerby Bypass and Improvements at Winderwath, Cumbria 2008 Tunstall Northern Bypass, Stoke A590 High and Low Newton Bypass, Cumbria A38 Dobwalls Bypass
This updates the table provided in my answer of 22 October 2008, Official Report, columns 415-17W.