Yell.com advertise local taxi companies for Egham and the Transport for London website provides some excellent advice on how to get around London via taxi or minicab. Please take a look and read any relevant information before you travel.
Normal rates from Royal Holloway to Egham should be £5-6 and from Royal Holloway to Heathrow should be £18-22 depending on which terminal you require. For journeys out of Egham, it is advisable to agree a price with the cab firm before you depart and share your journey with a friend if possible.
If you’re being dropped off by a taxi or Uber, your driver can enter the campus through the main gate. There is a drop-off area on the left, opposite Founder’s Square.
The vast majority of taxis are safe, but you may want to take a few precautions, especially if you're travelling alone. For example, only use registered/licenced vehicles and operators have your money ready before you reach your destination, get out of the cab and then pay the driver. When booking a cab you can also ask what sort of car will be collecting you.