Coventry City Council had declared their interest but all this did was to persuade members of Birmingham City Council to back plans for the scheme which will take the capacity up to 25,000.
Local residents are still unhappy and the Government will now decide if the plan can go ahead.
Warwickshire meanwhile, were involved in an abandoned Friends Provident Trophy game against Somerset at Taunton.
Marcus Trescothwick made 84 for Somerset but rain stopped play and the match was abandoned with Somerset on 135-2.
In the second test match at Chester Le Street, England closed on 302-2. Alastair Cook was 126 not out with Ravi Bopara making 108.