Work on the platform extensions at Parkway was well under way when I flew into Luton a few weeks ago.
Just to clarify on the Thameslink project: it's only the short stub of line between Farringdon and Moorgate which is being closed. This is necessary to allow the platforms at Farringdon to be extended (across the junction) which will allow most or all trains to be lengthened to 12 carriages. Trains only run down this stretch every 8 minutes or do and only during the peak... by closing the branch, up to 24 trains an hour will be able to run straight through between north and south London. Of course, anyone for Moorgate can change at Farringdon onto LU services.