What you can do right now:
Reduce the amount of paving
Even a slight reduction in the amount of garden paving can help reduce water runoff.
Replacing paving with plants, trees, and hedges can help moderate heat in summer and even provide better protection against the cold in winter.
Switch to a permeable paving option
Replacing your current paving with a more permeable option allows rainwater to drain more naturally and helps prevent runoff that can lead to local flooding.
This article from the RHS has some great advice on more permeable options like matrix pavements.
Remove all unnecessary paving
Any paving, even permeable options, is space that isn't being used for plants - reducing all unnecessary paving and replacing it with plants can help increase biodiversity and can even help regulate air temperature.
Car parking space is often the cause of excessive paving, if you need to park your car in the front garden: have a look at the minimum amount of paving you need to park the car on. The space between car wheels can be used to plant low growing plants instead.
Why is this important?
Climate change brings with it a higher change of rainfall in some areas, and with that rainfall comes an increased risk of flooding.
If rainwater is falling on more and more impermeable surfaces it's simply going to run off and increase pressure on local drains which increases the flooding risks further.
Replacing paved areas with more permeable options or better yet: plant life, helps absorb more rainwater and reduces runoff.