They are narrower than other stock but I think the reason you couldn't have the electric trains was because the route wasn't electrified (the Marshlink line stil isn't as far as I know).
That's only the half of it.
When the line was built in the 1850s the builders scammed the railway company by building thin tunnel walls to save money on bricks. One of the tunnels collapsed. So the walls were thickened with extra bricks. But the bricks were added on the inside. Putting them on the outside would pretty much have meant building all seven tunnels all over again, closing the line for ages.
So the tunnels became too narrow for most locomotives. This was OK in the days of steam, because there were a few locos skinny enough. But when steam went none of the diesels would fit. So in the 1950s BR built the Hastings diesels specially for the line.
Fast forward a few decades, and modern electric stock is too wide for two of the seven tunnels, and nobody will invest in widening them. So the diesels have to keep running for far longer than envisaged.
Eventually they become too unreliable, so in the mid 80s the line just HAS to be electrified so modern trains can be used. But there's STILL no money to rebuild the tunnels. The solution is to rip up the double tracks in the two narrowest tunnels and replace them with a single line. Which means the new electric trains can't go any faster than the diesels. The fastest morning commuter service from London to Hastings still takes 100 minutes for the 65 mile journey. It's quicker to go on a 30 mile diversion by taking the Marshlink line to Ashford and changing to a Javelin.
Which is why Hastings has been dying a slow death for decades instead of becoming another Brighton. Bad news for property developers but good news for long term benefit claimants and smackheads. There used to be lots of TEFL schools which livened things up a bit. They all moved to Brighton. There's still a successful art college and a small bohemian community living in very grand houses near some beautiful countryside and decent beaches. If you don't mind the needles or the lack of decent shops, cinemas, cafes and restaurants it's not a bad place to live.
Amazing what social changes have resulted from the absence of a few bricks.