It is very simple for BOOKED workings, no need to faff around with exporting data.
Do not use RTT for this.
Use OTT.
It will list the workings from a single platform for the period each train is booked to do it if you set the right search filters.
Go to the "advanced search" page.
This has one search filter by default but you need two filters - station and platform.
Use the TIPLOC for the station you want i.e. TIPLOC equals LUTON .... for Luton obviously
Then Add a second filter, select platform, and input 1 ... for platform 1.
That will return everything booked using Luton platform 1.
If you now want to look at platform 2, just change the 1 to 2 and hit search again.
etc.
I don't know how this works w.r.t. to last minute platform changes, but I doubt it is much different to RTT if it is a last minute switch at the immediate set of points further out.
It will certainly work if you are looking for trains into little used platforms e.g. try BOMO 4 for Bournemouth platform 4. That's the location I used to figure out to do this, as I was curious to know if 4 is still used as a platform in the sense of platform for boarding and alighting (as opposed to merely running through it from 3.
For the requested question at Bham NS platform three, you need TIPLOC = BHAMNWS and platform =3.
Likewise Reading 12 use RDNGSTN 12.