As others post, the general limit of 25MPH is for several good reasons and any general relaxing of the limit seems unlikely.
I can however see the potential for enhanced speeds in a few special cases.
As the national network evolves, more and more RELATIVELY modern stock is going to become surplus to requirements, and some will no doubt end up on heritage railways, in some cases this would permit of higher speeds in safety.
In not many years time, some HSTs are going to be withdrawn from the national network. They may well appeal to heritage lines, they are already borderline heritage ! Remember that the first ones ran only a few years after the end of steam.
HSTs already have central door locking and other modern safety features including improved brakes. In many cases I believe that an HST at say 40MPH would be no less safe than a steamer and wooden bodied vaccuum braked coaches at 25 MPH.
On the West Somerset Railway, during the summer season, the First train of the day from Bishops Lydeared to Minehead is regulary overcrowded with families spending a day out at Minehead.
I strongly suspect that a market exists for a fast service in that case.
Consider for example a preserved HST leaving Bishops Lydeared at 10-00 and running non stop to Minehead, which at a line speed of 40MPH would be reached in about half an hour.
Then at say 10-10 a steam hauled all stations service, limited to 25MPH could follow, this being the choice of those who prefer the sounds and sights of a "proper" train.
If of course the fast train could start from Taunton, that would be better still !
Another possibility would be a preserved HST for wine and dine services on heritage lines. There should be enough otherwise redundant HSTs to make a couple of sets with two kitchens, and all first class seating.
Ironically the West Somerset Railway is unique in operating under a Light Railway Order which specifically allows dmu passenger trains to run at 40mph rather than 25mph. But in practice this has never been implemented for all the safety reasons that have already been mentioned in this thread. The extra costs for central door locking, TPWS etc are simply not justified, although AWS has now been installed throughout and is operational on the dmu.