If its just legs and belly that are wet and dirty, I use an absorbant sponge/cloth to get the excess water and mud off and then let Humphrey dry naturally and brush out later. I don't think the one that I use is available in UK but I've find a similar sort of thing on Amazon UK, so you can see what sort of thing they are. This is 's the link:
Easidri Pet and Equestrian Grooming Towel for Dog/ Horse/ Around The Home, M, 68 cm/ 43 cm.,
I'm really impressed with them, - you can rinse them out or machine wash them and use them over and over, We keep one in the car.
I had to shower Humphrey this morning as he'd been rolling
, so got the worst of the water off with that and then wrapped him in a micro fibre poncho. If I use a dryer, I use my normal one but try not to do it too often as I'm worried about drying the hair out too much.