Conservative chair Sir Patrick McLoughlin insisted he’s not banking on winning seats in Birmingham.
Sir Patrick said he was delighted with the mayor result, in which former John Lewis boss Andy Street became the first ever mayor of the West Midlands - but he pointed out that the mayor election was on a very low turnout.
And he said there was no guarantee that the results would be similar in the general election, when turnout is expected to be higher.
The Labour candidate got more votes than Mr Street in Birmingham, but a detailed breakdown of the votes shows that the Tories won in the constituencies of Edgbaston and Northfield, and came a close second in Selly Oak and Erdington.
These were all won by Labour in the last general election. And it suggests Conservatives could have a good chance of taking some seats from Labour in Birmingham.
But Sir Patrick said: “The Andy result was a fantastic result. I think Andy will be a great voice for the whole of the West Midlands.
“But the turnout in that election was 25 per cent.
“So therefore, although we did incredibly well there and we won the mayoral election, it was on a low turnout. The turnout in the general election will be much higher.
“We are not taking anything for granted. We are working hard in Birmingham and we’ll see what happens.”
Conservatives won only one Birmingham constituency in 2015, Sutton Coldfield, a safe Tory seat which they are almost guaranteed to retain.
Sir Patrick insisted Theresa May had been right to call a general election to strengthen her hand in Brexit talks with the rest of the EU.
“Calling this election for June 8 was really the only time you could do that over the next two years.
“Because you’ve got the French [presidential] elections which have just taken place.
“And the new French Parliament to be elected in four weeks time.
“You’ve got the German elections in September.
“And then I think the real negotiations start to get underway.
“And that’s why I think this is the only opportunity we would have had to have a general election.”