The overnight timetable retains the same Bedford to Three Bridges half-hourly mainline services. There is no mention of any other overnight services, e.g. from Peterborough or Cambridge; although it does say that "Late night trains (departing between 23:30 and 05:00) are subject to further consultation."
All-night trains have been a feature of Thameslink since as long as I can remember; and I believe the line is unique in the UK in this respect. What was the original rationale behind the all-night service? If it's just to serve the airports, isn't it odd that the neither the Heathrow nor Gatwick Express services run all night?
If I could understand the original motivation, I could take a guess at whether we'll see all-night trains on any other Thameslink branches (or indeed on any other Govia services).
Southern used to have overnight services every hour, every night between Victoria and Three Bridges (with a few extended to Brighton). There was a lengthy thread on these forums - as well as much discussion amongst employees internally, many of whom were affected in getting to and from shifts - when this service was reduced to weekend-only (Fri->Sat and Sat->Sun nights), which is how it currently stands.
The supposed rationale for the reduction was to allow extra engineering works to fix common faults which could hinder the daytime service, but TL run over much of the same infrastructure every night and have encountered few if any difficulties (with the "headways", or time between services, easily allowing a further 1 train per hour, as existed before), and extra works have been both minuscule in scale, and few and far between. (There was also a suggestion that the reduction in service was only for six months or so - we are about to come to the point where we'd hear about services reintroduced, yet there have been basically no reinstatements put forward so far!)
The Bedford - Three Bridges service, as now, is not half-hourly through each night, but it would be good if this were the case. There has been a trial of a uniform half-hourly overnight service from St Pancras northwards, and I think all are awaiting the results of how successful that's been.
Compared to Southern, Gatwick Express has been similarly decimated overnight. There used to be some pretty useful departures when there were few other quick alternatives to get to the airport for an early flight - now, it can seem the choices are rather spartan. The drivers are also not trained to navigate around so many critical areas where engineering works could be (especially overnight), as Thameslink and some Southern drivers are, because they have lost the "route knowledge" of a whole host of diversions round South London, instead gaining the route down to Brighton in the daytime, which was previously crewed by Southern, with crew changes en route.
Other Govia / Go Ahead rail services may not be conventionally "overnight", but both London Midland and Great Northern do at least run some trains so early and late that they may as well be, just without trains running consistently both north and southbound through the whole night. There are also some overnight local services provided by GWR between Reading and Paddington, and on Transpennine routes in the North of England, mainly related to Manchester Airport and between major towns and cities.
I think it is anyone's guess whether the service on the Great Northern routes transferring (in whole or part) to Thameslink will ever be run overnight at a slightly more uniform and sensible frequency in both directions. The Southern and Thameslink services have had considerable tourist potential between London and the airports, and vice versa, as well as transporting shift workers to and from London suburbs. This sort of thing can make the service viable, and a careful study would be needed to make sure the service wasn't quite literally a case of fresh air being carted around. An overnight service, even hourly, as far as Peterborough or Cambridge would still need quite a few units and crews, with associated expense and resourcing (eg. work rostering, with possible new night shift volumes) issues. You have to also pick and choose which towns you should serve, which are viable for use by sufficient passengers, and whether station staffing and dispatch procedures will need to be changed.
There is also the issue of overnight engineering and diversions to consider. GN is not the worst off when it comes to this, but a lot of railways would struggle with being able to divert around track maintenance. The moment you put a bus on duty instead of a train (especially with a time penalty, bearing in mind London's convoluted road system), fewer people will use it, so it's no good just saying you'll run road transport instead.
Once you commit to running anything beyond an experimental service, people also start to rely on it more and more, which is not just an issue when you start to do replacement transport, but also if you have limited capacity which is not expanded on (say) Friday evenings, or if you withdraw the service as Southern did. Anything not specified by franchise / management contract obligations could be difficult to oblige the operator to keep running!
Timetable consultations I've seen do seem to want to work more closely to a standard "clockface" template throughout the day, ranging from early morning to late evening, against the current mashup of stopping patterns which plagues Southern and Thameslink during peak hours, and massively hinders reliability and service recovery. I would say this is hopeful for forming an easy-to-use base for rolling forwards and backwards into the smaller hours of the night, just sequentially adding more trains into the plan, but how quickly this can happen is pure speculation.
