for tgi's i just submitted my cv and wrote some waffle on my personal statement. i put that if the position i applied for was unavailable, then i would also be a good fit for any other roles going. i wasn't really bothered about the tgi application because i got rejected from there earlier this year, i think it's mostly down to luck.
tesco is harder bc their little screening quiz bc some of the answers that seem really obviously right are wrong. i honestly just looked up tips on how to pass it (someone mentioned that you have to answer according to customers being number 1 priority, teamwork e.g. helping other colleagues at number 2, and your own work last, which seems to work bc i passed the quiz.) once i did the quiz, they asked for proof of right to work and set up an interview after about a week.