Tenderise the meat first, as rump can be quite tough. You don't have to buy a tenderizer, just use your knuckles to 'knead' the meat.
To cook it, heat a frying pan until piping hot (no oil) and then add the steak (season as required). Turn ONCE only. If you want it rare 5 mins will do, if you want it medium/well done then up to 10 mins.
For the mushrooms, try baking them in the oven for about 15-20 mins in tinfoil with a knob of butter and plenty of freshly ground black pepper. Or better still, quarter them and cook in a saucepan with said butter/pepper but add sliced onion. Delicious!
Enjoy. x