He's been automatically added to the waiting list since national offer day. It's a good time to find out where he is on the WL because, as appeals draw to a close, some may withdraw their places in favour of wherever they appealed for. Summer of Year 6 is also a prime time for people to move home altogether, which means that (hopefully) they will notify the LA of their move and new school place.
Other key times for places to open up are the second week of September, as movers are confirmed as attending their new schools, the end of September when others go to school that now have places that opened up a fortnight ago, and in the New Year.
You may need to confirm that you wish to stay on the waiting list or reapply as an in year admission after Christmas, depending upon whether the LA wipe everybody off the waiting list once the legal requirement to maintain it expires.
Unless your DS has particular SEND that makes it impossible for him to make his own way to and from the school he is allocated (because you do need to accept whatever you are offered), your driving is neither here nor there.
Depending upon the size of the intake at the school you want, it wouldn't be unusual for 5-10 to move over the summer or not turn up because they have places at private or miles away where they've moved to. In addition, 2-3 going at the end of September wouldn't be a surprise.
A lot of people who are still on the waiting list come September will, if offered, decline it, as they've just started, bought the uniform and so on, which also increases the likelihood of being high enough up the WL to be offered a place.
At no point does an email from the local MP make even the slightest bit of difference. The Law requires that school places are offered in accordance with the determined admissions policy and the legal oversubscription criteria. In short, nobody working in Admissions, nor their Headteacher, Chair of Governors, Parish Priest or pet cat pay the slightest bit of attention to whatever their constituency assistant has typed up for you. If they did, it would make a mockery of the Law - and would inevitably lead to mates of the MP being able to get their kids into the most oversubscribed schools at the expense of everybody else being treated fairly. If anybody ever claims it happened because their MP got in touch, they're experiencing real life correlation =/= causation; it's a pure coincidence.
It's tough and it's nerve wracking, and it's probably a bit scary thinking of your child travelling to school alone on the bus - but if you have been unable to evidence circumstances that made it necessary for your preferred school to offer him a place, it has been dealt with correctly and your choice is whether you equip him to go somewhere else and thrive whilst waiting in hope of moving up the waiting list or whether you contribute to his distress by focussing on something that the Law shows isn't feasible. For your DS's benefit, making the best of it is better than catastrophising.