Hello! I'm a PHP developer freelancing in the UK. I can complete this project for you in 30 days, possibly even sooner. I will be using a custom codebase, as I believe this is the easiest to maintain and most secure. I'm proficient in creating smooth user experiences with a mixture of fluid programming and pleasant, clean design standards.
I would create the system like this - cab companies sign up to use this service, and then on the front-end regular clients can select where they would like the taxi to pick them up, and take them to. It would calculate a cost by milage pre-defined by the taxi vendor, and then send off details of the order to the taxi vendor. Email confirmation with details sent to the taxi user. Payments would be handled with stripe.com.
I can start developing this straight away, and it sounds like a fantastic project. Please feel free to send me a message on Freelancer if you have any questions on how I'd implement the solution, payment enquiries, or anything else.
Regards,
James