I’m agreeing with you. That is not the backdoor to No. 10 but it appears Justin was forced to hoof it some distance rather being driven up to the door.
10 Downing Street looks more like what I would call a wide alley than a street. There are gates to restrict entry into the street. I am guessing Castreau was driven there and then got out of the car to walk up to Johnson for the cameras — more video-friendly than having Fudeau let out at the front door.