AGree with foxinsocks.
The privately-educated kids of my acqaintance get faaaar more homework, but most of it seems to be either very routine (pages and pages and pages of practice in letter formation for a reception child to be completed over the halfterm for eg) or sufficiently complicated to require major parental input (eg. Y2 child being expected to spell words that they couldn't possibly have any practical use for such as 'secretary', 'protracted', 'concede'. And endless endless drilling on times tables.
Obviously these kids may, on some measures, be two years ahead of their chronological age, but pushing a child beyond their ability is not ultimately sustainable, nor is it particularly useful. And it takes up a lot of time in which kids can be doing more fun and independent things.
DO NOT BE FAZED by people whose kids are/seem to be performing way beyond your dc. As long as your dc are learning to read well, and to learn basic maths, everything else is mostly fluff and can be easily replicated at home by taking them to museums, castles and the theatre. Give them lots of books, and talk to them a lot. That way you end up with dc who may not be quite as impressive in terms of joined-up writing, but have lots of ideas and things to say for themselves, often a bit more left-field than the more intensively-taught kids but none the worse for that.
Truly, do not stress about it. And remember that people who are paying £12K a year for a primary education have a vested interest in believing that the system they're buying into is better, so develop a good bullshit filter for some of the wilder claims you'll hear.