First I thought this thread was about height. Then - oh, never mind.
Seriously: if you plan to carry it on while departing the UK, it has to fit into a 22" (56 cm) long sizer. That includes wheels and handles. The sizer's other dimensions are 17.7" x 9.8", so we're talking about a pretty small suitcase here! (Don't count on wiggling out of this based on class of service, elite status with any airline, or anything else short of a royal title - which is no guarantee, either.)