It shouldnt be too difficult and a nice project to learn some useful stuff:
You need variables from the client:
Where are they from where are they going? So you need their pick up point and their destination - send to application to calcute distance.
What time do they want to travel? So put up a date-picker and time and you've got their time of travel.
and variables/constants from taxi firm:
What do they charge per mile (pence per mile), do they charge extra on-peak/off-peak and do they charge more over a certain distance, do they charge to return to depot if long distance (extra costs)
So we have: distance x pence per mile = quoted cost
or if time of day = on-peak: distance x (pence per mile + extra costs) = quoted cost
Dead, dead simple but really effective if you can source the data you need properly, the data might be worth paying for, but this link looks useful on the face of it. Distance Between Full UK Postcodes
About a grand if they are a wealthy company (as this might be more realistic, timewise) but you have to swing with the punches sometimes and do it for cheap if they haven't much money. This would be a good example for a portfolio so you have to think of that too.
I'd be interested to see what other people would quote too...