My office cab was half an hour late.

[tufguy]

Please check my sentences.

1) My office cab was half an hour late.
2) My office cab was late by half an hour.

 

[tedmc]

They are fine. Does the cab belong to your office? I find it strange that an office owns a cab.

 

[emsr2d2]

My cab/taxi to work was half an hour late.

As ted said, "office cab" isn't natural. In the case of your sentence, there's no need for anyone to know who booked/paid for the cab. The only relevant things are that the cab was taking you to work and it was late.