Do SATs results determine sets for English and Maths in Year 7?

Private Primary schools don't even bother with sats and parents have the right to withdraw their children from taking them. So a Secondary wouldn't be able to use the results for sets as not all year 7s will have taken them.

SAT results are used to generate GCSE targets in ALL subjects so they are really quite important in that respect . This is then how ofsted measure the success of secondary schools. When the word 'progress' is used in ofsted reports, it refers to whether the child is likely to achieve their GCSE target which is generated from the SATs score. Schools can increase these targets but are absolutely not allowed to reduce them. The secondary school has no control in this respect. In regards to the new SATs scoring 100 is the average score, anything over 115 is considered 'greater depth' and means it is likely the child will have GCSE targets of 8 and 9s. In old money, 110+ would be level 5, 100 to 109 level 4 etc

Ours used CATs and a placement test to set after the October half term. SATs say more about the school, and not necessarily about the quality of teaching.

SATs are checking up on the school
not the pupil
Secondaries quite often totally ignore SATs
stress not

They did for both my DS who were placed in th top set at secondary and despite retesting them all there was very little if no movement. DS1 took the old SATS and got a 5, DS2 was the first year with the new SATS and scored 117. I gather he's in the top third of his class but by no means the best.

As well as it depending on the school as to whether they use SATs results to set (adding another "DC's school doesn't here) it will also depend on the school what the standard is for the top set(s). It will also vary between schools whether they set in strict order (so set 1 is higher than set 2 is higher than set 3 ...) or whether there might be 2 different set 1s or whether the school might timetable and set within (say) 3 strands.
Above all, I'd query why you are even asking? Your question should be (once your child has actually started) "is my child in the correct set for their abilities? Are they being taught at an appropriate level?" Also bear in mind that the school may use the first part of year 7 to recap and ensure everyone has covered the same material. They may not be covering new things (or being stretched) at first.

It depends on the school, if you need to know for sure I'd ring and ask them once the new term starts

Not in our school. They retest kids at some point in the first term and usually set after Christmas. They only seem to use SATs results as a guide for whether the child is tracking a similar level as they go through years 7 and 8. Adding to predictions from their own testing and classwork along the way.

Some schools do CATS.
Some schools do mixed ability sets for between half a term and the first year to decide sets, some do mixed ability forever.
Some use SATS, catchment will have a huge effect on what scores get you in the top sets.

It depends on the school
they each do their own thing
and it varies year on year
and the amount they reshuffle sets each term varies between schools and across years