There are about 29.9m homes in UK
Adding 1.5m homes is roughly 5% increase.
Whilst completely new towns are logical, even building 15 towns of 50,000 is only half number required (and most UK town are nearer only 10,000 homes). Might have been better to also say every town, village, hamlet has to add at least 3% to number of homes and anyone blocking a site within the 3% has to put forward an alternative site.
But let's get away from off topic discussion about tax
The thing is there's already a number of homes in the pipeline, let's say that's 200,000 per year, then you're about 1 million over the next 5 years.
Some areas have areas that could be brought forward, from their expected delivery timeframe, let's say you could bring forwards anything from year 6, that's 1.2 million (average of 240,000 per year).
Allowing stuff an easier path through planning isn't likely to make much difference this parliament, however could allow the delivery of (say) 320,000 per year over the following 5 years. That would get us to an average of 320,000 per year.
We could probably add new towns to that, at 5,000 homes per town (population of 12,000), you'd need 40 new towns over the next decade to reach the average of 300,000 per year. That would average at slightly more than one per county council (there's 29 county councils and 6 metropolitan counties).
12,000 is about the size of Bodmin, Haslemere, Henley, Bolsover, Littleborough, Thorne and the like. As such, not large places, but still quite significant in a location which may not have all that many people currently.
However, are of a size that most facilities could be delivered within their boundaries, meaning that (except for perhaps collage) most school and extra curricular activities could be undertaken without having to travel beyond the new town, which would reduce the impact on the existing road network. Obviously this would still take a lot of travel for work, although some of that could also be internalised (such as school teachers, shop staff, leisure centre staff, restaurants staff and the like).