Inevitable.
As a result of the last twelve months tax is going to have to go up by quite some amount in many areas. The balance the Tories have is that the extent of the problems have been to a great degree of their own making. People will remember and be upset at paying because of their lack of early action and the consequential costs. The problem here is taxing new cars, especially of British manufacture. That will hurt the economy even more. This drives more to road usage based pricing. Easily done through MoT records (although I am sure some will try to by-pass that by disconnecting the trip in some way). Your next year is based upon your previous history and then corrected at the next renewal.
BiK has to be reintroduced at a level directly commensurate with private ownership. That includes, vehicle cost, cost of insurance and maintenance plus a factor for having someone else look after your car affairs. Job need for specific reasons has to be factored in of course but most company vehicles are just perks providing a clear cost advantage. On the opposite side, 3 year plans continuously push new sales although often heavily discounted.
I think a choice between road-based-pricing plan (based upon car value and environmental impact such as current road tax) where lower usage is rewarded and a straight higher Road Tax to reflect the potential higher usage is likely to be what happens. Drivers will choose the best for themselves and potentially look at how much they drive with a little more critical view. The reality is that the costs will likely still be way less than using public transport (even with city based zones) which is itself a major disincentive to do that.