As Mandy Rice Davies may say, "we he would, wouldn't he?".
Of course a BR Chairman is going to say something positive (even if he knows that the numbers aren't looking good)
The rubbish ones like Dr Beeching didn't
You need a better argument than "ah, but Beeching/Serpell".
If Reid had inherited the same mess of hopeless lines that the Good Doctor had to deal with then similar cuts would have been made - the fault was with the Victorian speculators and the fact that many of the lines that they built were only useful in the days when there was the freight to sustain them - once that freight dwindled, there was no point to keeping a lot of the lines open. Not Beeching's fault - Reid or anyone else would have had to make cuts (however much it might make people feel more comfortable by pinning all the blame on one Scapegoat)
What nonsense to say that the line couldn't be operated viably by train. It would be an extension of the existing service, which would be rather better used at its southern end than it is now.
...and there's the problem - it'd be a ten coach train running from Uckfield to Brighton (if it's to be an extension of the London - Uckfield services, since that's what the service was pre-COVID, I think it's a fair benchmark of what length the Uckfield - London trains will need to be by the time that any Lewes extension happens) - and there's really not the demand for that length of service between Uckfield and Brighton - even if it were one of the few times a year there was a B&HA home match on.
So your proposal is already hamstrung by the need for such high running costs, and that's on top of the several millions of pounds on additional carriages to provide the service south of Uckfield (I think that a new EMU carriage is over a million quid nowadays, but happy to be corrected)
Even if the line was built for no cost (although I suspect that this is going to be another one of those threads where people suggest a cheap re-opening which entails single track sections but can also miraculously accommodate all of those diverted trains on the rare occasions that a parallel main line is closed...)...
...your probably going to struggle to run an hourly Uckfield - Brighton - Uckfield service with just one (ten coach) train - especially given the pressures on platforms at the Brighton end - so how many additional coaches are you going to need? Twenty? Plus a handful of extra ones to cover maintenance (say 10% more)? That's best of twenty five million quid just on the trains, before you factor in the cost of running ten coach trains all that way for the low number of passengers. Yes, there's a bus service from Uckfield to Brighton (currently half hourly? I can't tell if that's a reduced "Covid" service though) but that runs by different routes (which indicated that demand is spread thinner than just one corridor), that also includes the Tunbridge Wells - Brighton passengers - a train would have to run via just one route and wouldn't include the passengers from Tunbridge Wells. And, as you want an extension of the London services, that train would need to be ten coaches long.
Even if the plan is to replace some existing Lewes - Brighton services, you're going to struggle to match the London - Uckfield paths (which are seriously limited at the London end and through the East Croydon bottleneck) with existing paths from Lewes into Brighton, so will this mean an awkward wait at Lewes for your ex-Uckfield service to slot into the path of a Lewes - Brighton stopper?
And even if you want to replace some existing Lewes - Brighton services to reduce the number of additional carriages required, you're still replacing a three coach 313 with a ten coach EMU (of whatever class TSGN have to order to accommodate this newly electrified line). Presumably all of the local stations on the East Coastway can accommodate ten coach trains, or will you require platform extensions too? Uckfield - Brighton - Uckfield will be too long for an hourly train to run with just one ten coach unit but Uckfield - Lewes - Uckfield would be too quick for an hourly train to run with just one ten coach unit (i.e. if you were going to run onto the path of a Lewes - Brighton - Lewes stopper - and that's assuming that a London - Uckfield - Brighton - Uckfield - London service, which must be knocking on four hours, can have a reliable turnaround time at Brighton in the same time that the short Lewes - Brighton - Lewes shuttle can cope with).
The more I look at it, the worse it gets. NO wonder the people "actively campaigning" for fifty years haven't convinced anyone important.