Luton to Milton Keynes sees its heaviest traffic on weekday mornings and early evenings, when the M1, A1(M) and M25 are shared between commuters and airport travellers. If your journey falls in one of those windows, building in some extra time is sensible; outside them, and at weekends, the roads are typically quieter. Either way, the route is planned around the traffic on the day, not around a fixed schedule that ignores it.
The pickup point is settled in advance so there is no confusion on the day, and any airport leg is flight-tracked, meaning the car follows your real landing time rather than the original schedule. Either side of the drive, expect the usual airport process — check-in and security outbound, or passport control and baggage reclaim inbound — both allowed for in the included waiting time.
Telling us your group size and luggage at booking, rather than leaving it to the day, means the right vehicle is waiting: a saloon for up to four people and two large cases, or an estate, MPV or 8-seater for more bags, buggies or equipment. Journeys like this get busier in school holidays and summer, so booking ahead is the simplest way to secure the size of car you need.