London Stansted to Tooting Broadway?Watch
You can either buy one ticket for the whole journey or use Oyster/contactless until you get to Tottenham Hale and buy/have a separate ticket ready for the Stansted Express.
If you're travelling to Tooting Broadway for uni in August/September, then check timetables closer to the time, as more services may be reinstated by then. If you need to travel soon, then rockrunride's suggestion is definitely the best. The Stansted Express is every half hour and the Underground is still very frequent.