I’ve been for a few.
NHS van - go to changing room, remove bra but keep on top. Wait in private waiting room. Privately escorted to mammogram room, door locked, remove top and put on hook opposite side of room to machine, but room is tiny so only 5-6 steps to machine, really no need for gown, crossed arms across my chest and technician made it obvious she was busy looking elsewhere. Once done put top back on, escorted privately to private changing room to put bra back on.
NHS clinic - Given a half length gown and basket. Top half clothes into basket and put on gown them wait in public waiting room. Walkthrough public area to mammogram room, then back to public waiting room, same for ultrasound, then for physical exam, then biopsy, in public areas with gown all while carrying shopping basket around.
Private clinic - Go into mammogram room. No changing cubicle. Remove top and bra, put on chair opposite side of room, again room is small so not big deal. Once done have to awkwardly (I fasten at front and spin bra around large boobs jiggling as I go so 😳) put bra and top back on in room with technician.
Its not the nicest of experiences, especially with G cup, saggy boobs, but I felt least exposed in nhs van.