If you want a cheap flight from Teesside to Rio De Janeiro, you've got zero airlines to choose from.
Rio De Janeiro Santos Dumont Airport is just one of the airports in Rio De Janeiro. If you're not set on a specific airport, try changing your search from Rio De Janeiro Santos Dumont Airport to Rio De Janeiro to see a broader range of flights – they might be cheaper.
If you're planning on going to Rio De Janeiro during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.