Having had a total of three kids at primary school continuously over the last 16 years I'd say you HAVE to make an effort to talk to other mums, mix with them, go for and invite back for coffee, lunch, playdates etc. if you want your child to have a very active school social life.
Much depends on the mums, whether you like it or not, even if little Jonny likes your little Ben, if Jonny's mum isn't keen on either of you then the playdate invites will fizzle out after a while.
Its all pretty OK in YR and Y1 and for most of Y2, kids are pretty non-selective of friends and quite open to playing with all and sundry. By late Y2/early Y3 they do start to become selective about friends and who is good to be friendly with, and they will pick up on nuances from their parents about who is a 'nice' child to play with and invite home. If your child has some wacky behaviours, other children will rapidly get the message from their parents that s/he is not a nice child to play with and one to avoid.
Girls pair up often with that special 'best friend' by about age 7, whereas boys don't go for the 'best friend' thing quite so much and have friendship clusters, and in my experience ability at sport, preferably football is one of the useful things for them to have by around age 8 to get invited into playground kickabouts. As is parents getting involved at this age with local children's sports teams, being a helper or coach. If your child has no ball skills then be aware that just that may exclude them from inclusion the 'popular' group in junior school.
My experience is based on a small primary school in a pretty middle class area with a high proportion of SAHM's, the rest mostly working profs like teachers, nurses etc. And for some of these people they do actively involve themselves in directing their kids to mix with certain groups of kids, and the parents themselves mix quite closely; the walking mums (do their mile circuit after drop off), the lunching mums, the mums who are involved with the PTA, the mums who are Friday evening social gatherers and invite each other to dinner etc. They exist, and if you want to be part of it, effort in YR and Y1 is essential; they won't come up to you in the playground and invite you to mix with them, you need to make the effort for quite a while to be accepted into the group.