You need to present the existing MOT with the car so they can post-date the new one. Go somewhere that does ‘just mots’ and no repairs, as this means there is no incentive to fail it to create work. Unless you have too much cash/not enough time, in which case go to a normal garage where you can just forget about it till they ring you up with a pass certificate (and the bill).
KwikFit…”your car needs new front wishbones, that’ll be £600 please.” I told them I was coming to get it and sort the repairs myself. “But its in bits on the ramp!” OK…when will it be all back together, cos I’m not paying you £600!? “Ummm…” Took it down the road and an independent replaced the bushes in the wishbones, and charged me something like £80. He was obviously too cheap as he’s closed down now 🙁