There is more than one solution to this problem.
This is a way that I would recommend:.
Assuming ArcMap is your primary tool:
Open the attribute table of the network source features.
Add a field of type "Short" (any integer type will do). This will effectively be a boolean value. Give it a name that would describe it as a restriction.
For each road segment that meets your restriction parameters (i.e. motorways, slip roads) calculate that row's restriction value to be 1. All segments with a zero (or NULL) restriction value will be traversable.
Add this value as a network restriction attribute and use a "field evaluator". You will need to "rebuild" your network. (Alternatively, use the New Network Dataset Wizard to create a new network dataset)
Supplementary information:
Feel free to ask for clarification if you run into any difficulty =)
I suppose the first question is why you want so many routes to that precision? 8000 routes overlaid on one map is not going to look very pretty. Would you not be better just to draw straight lines? Is the actual route really that important?
There are a number of different problems with the approach you propose above - the first is going to be connecting the rail/subway and road networks together without which it can't be routed as a whole, which from your description above of data with modal interchanges, is what you need.
The next problem is, as you say, getting enough waypoints to force your routes to take a certain mode of transport. I guess you will probably need to get a mid point between each part of the rail network that is between an interchange onto the other network. But how do you stop road journeys routing onto the rail network (which is usually more direct)? You could add a very high cost for rail routes, but this might force some journeys to double back unless you got the waypoint right in the middle. And how on earth do you deal with bus / tram networks, short of adding waypoints for each route segment?
The final problem is processing time. Depending on the size of the network, it could be very high for the number of routes you are talking about here.
To be honest, I'm not even sure that the advanced and expensive transport modelling packages such as TransCAD / EMME3 have this functionality out of the box, as they are primarily concerned with modelled data, rather than real world data.
Bottom line is that it's possible I think, but will involve substantial investment in time to sort out the network and a heavy degree of programming before you can undertake this analysis.
Having said that, someone must have attempted this before. Which is a good argument to ask transport professionals, not just GIS people.
Best Answer
If you want Free (but you will have to do a lot more pre-processing) OS VectorMap™ District is available. https://www.ordnancesurvey.co.uk/opendatadownload/products.html
For commercial rotatable data you have 3 options.
Ordnance Survey - OS MasterMap® Integrated Transport Network™(ITN) http://www.ordnancesurvey.co.uk/business-and-government/products/itn-layer.html
(Many £££/$$$$)
TomTom (aka TeleAtlas)
http://www.tomtom.com/en_gb/licensing/products/maps/multinet/
or
Nokia (aka NAVTEQ® Map Data)
http://www.navteq.com/products_data_content.htm
from memory Navteq was the cheapest option, OS was the most expensive (os map data was 860% more expensive than the entire project budget).