I get a vibration in my stearing wheel when i press on my breaks when going above 60mph.

From what you have described the disc rotors on the vehicle are distorted and could be fairly badly distorted if they have been subjected to excessive temperatures at any time.

This will translate into a pulsation in the brake pedal - especially noticeable when you brake at speeds above about 40mph. At 60 mph - as you found - you cannot miss it. At higher speeds you will also get some vibration through the steering wheel once you brake.

The disc rotors will need to be examined and removed from the car for machining or total replacement. They may be too worn or distorted for machining as the manufacturers specify a minimum safe disc rotor thickness. Disc rotors don't last the life of the car and replacing them is a fairly routine exercise and not usually expensive except on many European cars and on many prestige brands.
The brake pads should also be replaced at the same time unless replaced recently and have minimal wear. The operation of the brake calipers should also be checked.

If you had a wheel balance problem on the car (rectified with a decent re-balance of both front wheels) you would find a constant vibration through the steering wheel at a given speed usually above about 45mph. What you have complained of is vibration only upon braking plus a pulsation through the brake pedal whilst braking.
However if you are also noticing a constant vibration through the steering wheel at or above a given speed when cruising you need to have the front wheels re-balanced and the front suspension and steering checked for problems.
If you have uneven tyre wear you will also need to have the front wheels re-aligned. If a front wheel alignment was not done on the car in the last 12000 miles it will need a wheel alignment in any event.

Cheers
Sean

YOU MAY HAVE DISTORTED DISCS, OR THE BRAKE CALIPERS ARE STICKING, OR A WHEEL IS OUT OF BALANCE AND WORN BUSHES,THIS COULD BE CAUSED BY DICS OVER HEATING, THEN HITTING A PUDDLE, IF YOU TAKE CAR FOR A RUN AND USE BRAKES HEAVER'LY THEN PUT HAND NEAR WHEEL, IF ONE IS HOTTER THAN OTHER THEN THAT COULD BE THE SIDE WITH PROBLEMS TO CHECK IS WHEEL OFF AND HAVE DISC'S CHECKED FOR EXCESS RUN OUT,