My 2 girls (both key stage 2) are tought at the start of 1 maths lesson a week, as a mental maths starter. They also work a 'league table' system - league 1 is 2s, 5s and 10s, Championship is 3s, 4s and 6s and Premiership is 7s, 8s and 9s. The order of the times tables are all muddled for them to fill in. They can then move to the Super league which is mixed of everything against a timer!
They actually began their tables in year 2 at least, possibly with 2s in year 1.
Personally I can mostly remember all of mine having learnt them 'by rote'. (They are also a great distraction at the dentist to recite them in your head during a filling, lol)