Maud, I have had recent rat trouble under my decking. Just as you need fuel, ignition and oxygen to start a fire, you need food, access and comfort to start a vermin problem.
Food first - as they don't really care what we think our boundaries are, it's the whole street's problem to remove food sources. You're quite urban as I recall so perhaps it's impractical to get everyone to not overfill their bins (making the lids useless) and for passers by not to drop food-based litter. In my area, I'm fairly sure that food left it for neighbourhood cats and dogs is the problem, plus bread for birds, and indeed the nice bird food and fat balls which I put out myself until I saw the light.
Access is what you're doing - ensuring fences and gates go right down to the ground, and If the ground is burrowable, put a barrier further down. My decking has panels on all sides which don't quite reach the ground (or they would rot). One side of my decking has a planted border flush with it - the rats actually undermined a rosemary bush so much that it died off. I've now got chicken wire fitted down the side so they can't burrow that way.
Finally 'comfort' which I mean as a catch all term for not having predators, having enough space to nest, and a reasonable level of dryness. Decking should always have gaps so that the planks can swell in wet weather. This also means it won't be dry underneath for animals to nest. The space beneath decking should also be filled as much as possible with ballast like rubble chunks - this is great for beneficial insect hibernation and nesting like beetles and spiders, and possibly solitary bees - but no good for rodents and foxes. In terms of predators, well, what can you do about the urban fox, they're almost untouchable! For rats I put down poison bait which worked but unless you also deal with access and food source some other wing of the family will just move in. I was hoping for the local owls to help me out and am still vaguely considering putting up a nest box in the trees close to my garden so that my rats are right in the food territory.
Unlikely to do much in the garden today - I am catching up with work because I am covering three jobs at the moment and mustn't drop the ball. My greenfingers order has arrived with the garden track so the boys may put it together later.