Barr will compete as part of the women's 400m relay team at the meeting in Annecy, France, on June 21-22.
Milton Keynes AC sprinter Craig Pickering has been named in the men's 100m relay team.
Dave Collins, UK Athletics performance director, sa
id: "In an Olympic year, the European Cup is obviously not top of our priority list, but it is still an important competition.
"We have selected the strongest team available to us and I expect many of our athletes to use this opportunity as part of their build-up towards Beijing."
Men100m: Tyrone Edgar (Newham & Essex); 200m: Marlon Devonish (Coventry Godiva); 400m: Martyn Rooney (Croydon); 800m: Michael Rimmer (Liverpool, Pembroke & Sefton Harriers); 1,500m: Tom Lancashire (Bolton Harriers); 3,000m: Andy Baddeley (Harrow AC); 5,000m: Mo Farah (Newham & Essex); 3,000m steeplechase: Andrew Lemoncello (Fife AC); 110m H: Andy Turner (Sale Harriers Manchester); 400m H: Dale Garland (Channel Islands AC); High Jump: Samson Oni (Belgrave Harriers); Pole Vault: Steve Lewis (Newham & Essex); Long Jump: Chris Tomlinson (Newham & Essex); Triple Jump: Phillips Idowu (Belgrave Harriers); Shot: Mark Edwards (Birchfield Harriers); Discus: Emeka Udechuku (Woodford Green & Essex Ladies); Hammer: Mike Floyd (Sale Harriers Manchester); Javelin: Michael Allen (Trafford AC); 4x100m: Harry Aikines-Aryeety (Sutton & District), Marlon Devonish, Edgar, Rikki Fifton (Victoria Park & Tower Hamlets), Christian Malcolm (Cardiff AAC), Craig Pickering (Marshall Milton Keynes); 4x400m: Tim Benjamin (Cardiff AAC), Richard Buck (City of York), Rooney, Andrew Steele (Trafford AC), Rob Tobin (Basingstoke & Mid Hants), Conrad Williams (Kent AC).
Women100m: Emma Ania (Shaftesbury Barnet); 200m: Christine Ohuruogu (Newham & Essex); 400m: Nicola Sanders (Windsor, Slough, Eton & Hounslow); 800m: Jenny Meadows (Wigan & District Harriers); 1,500m: Susan Scott (City of Glasgow). 3,000m: Helen Clitheroe (Preston Harriers); 5000m: Jo Pavey (Exeter Harriers); 3000m sc: Barbara Parker (City of Norwich); 100m H: Sarah Claxton (Woodford Green & Essex Ladies); 400m H: Tasha Danvers (Shaftesbury Barnet); High Jump: Susan Moncrieff (Trafford AC); Pole Vault: Louise Butterworth (Birchfield Harriers); Long Jump: Jade Johnson (Herne Hill); Triple Jump: Noni Mordi (Belgrave Harriers); Shot: Rebecca Peake (Sale Harriers Manchester); Discus: Philippa Roles (Swansea Harriers); Javelin: Goldie Sayers (Belgrave Harriers); Hammer: Zoe Derham (Birchfield Harriers): 4x100m: Ania, Montell Douglas (Blackheath & Bromley), Emily Freeman (Wakefield Harriers), Jeanette Kwayke (Woodford Green & Essex Ladies) Anyika Onuora (Liverpool Harriers), Kadi-Ann Thomas (Marshall Milton Keynes AC); 4x400m: Vicki Barr (Rugby & Northampton), Lee McConnell (Shaftesbury Barnet), Meadows, Ohuruogu, Marilyn Okoro (Shaftesbury Barnet), Kelly Sotherton (Birchfield Harriers),
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