First off you need to understand why are people driving and where to and then decide what you want to achieve - reduced congestion, modal change, cleaner air, climate change objectives etc.
The problem with modal change is that things like walking and cycling are great when the weather is nice but tend to suck when its pouring with rain. Public transport is woeful with limited destinations, erratic availability and it often just works out cheaper to drive. As noted there is a total lack of safe cycle routes and the roads are in such poor shape that cycling can be downright dangerous with the many deep potholes and sunken drains at the side of the roads.
Some ideas:
Improve cycle paths where possible and failing that improve the edges of roads so there are fewer pot holes, dips and sunken drains. increase places to securely store bikes as well, no point everyone cycling if, when they arrive at their destination, the bike gets nicked!
Increase frequency of public transport during winter months and try and expand the network (I realise that is potentially very expensive). Look at costs of public transport and compare to cost of driving. If it isn't cheaper then people won't use it and If you can't make it cheaper then you are doing something wrong.
Look at slowing traffic down (controversial I know) so that it reduces the danger to cyclists and other road users such as electric scooters if they get introduced. Pedestrianize town centres (may help improve the retail experience as well).
The reality is however, that people are wedded to their cars as they are so flexible. So there needs to be a push to at least go electric. Look at dedicated electric only parking spaces, increase charging infrastructure (encourage businesses and hotels to install them), free parking. Make petrol cars less attractive - higher parking charges, charge to enter towns/villages. This would need the co-operation of the surrounding authorities to ensure they do the same so that people don't just all go to Southend or Basildon. It also needs the changes to improve cycling/public transport to be implemented so that people have the choice, especially for those that can't afford an electric car yet