I would not really change it - it was fine as it was for the roles that it was used for
Very mobile and relatively light - ie a bunch of muddy squadies and some kind words would get it moving again if it did get stuck
During the BEFs short stay in Belgium and France in May 1940 its division and Brigade level Carriers often made the difference between the British getting to a Bridge or Cross roads first before the Germans cut them off! Often they were used to quickly move the Vickers MMG teams to cover gaps that suddenly opened up slowing down attempt to flank etc.
Also it was cheap - and relatively easy to replace, transport and maintain
I would however make a larger version complimenting the Carrier family capable of transporting 10 men, their equipment plus a driver in some discomfort. Can also be used as a gun tractor, combat engineer vehicle and tracked ambulance
Something like a larger Lloyds Carrier - perhaps a 3 bogie affair?
Front Engine - high sided with a rear door (Hence the Front Engine) - canvas top with 'hoops' to allow head room etv
Again its a transport not an AFV and while it can mount a units Bren or Boys ATR or even a Vickers MMG its job in battle is the move the troops quickly to a forming up point before retiring to a vehicle laager (is that how its spelled?) where it will wait often with much of the sub units kit - such as overcoats, Bren Cleaning kits spare ammo etc while retaining simple maintinence and decent cross country ability.