They do look narrow, though reminiscent of the island platforms at Clapham North and Clapham Common on the LU Northern Line. If anything's going on in Clapham, these stations can quite often be closed due to overcrowding on the platforms.
In more recent times heavy reinforced glass walls have been put in at very busy points in the city centre such as Buchanan Street and Hillhead where there is an island platform and a side one. Not before time due to heavy use.