Ah, the good old TS2, advanced for its time but a stillborn project as it was canned by the Labour government of the day. It's interesting to see mention of tantalum capacitors being used on the TSR2 but hardly exclusive to the electronics only as Tantalum has been used extensively in the superalloys used in jet engine manufacture since the 1960s. The very high melting point of tantalum (3017°C, 5463°F) helps strengthen the superalloy and guarantee long service times.
Going back to tantalum capacitors though, which are typically made by sintering tantalum granules together then forming a thin dielectric layer over the outer surface by a chemical treatment. This layer is thick enough to avoid breakdown at rated voltage - and thin enough that it will be punched through by voltages not vastly in excess of rated voltage. For a 10 V rated cap, operation with 15V transients can cause catastrophic failure.
Unlike aluminium 'wet' electrolytic capacitors which tend to self heal when the oxide layer is punctured, tantalum does not tend to heal. Small amounts of energy may lead to localised damage and removal of the conduction path and as the damage is cumulative, a stage is reached where a low resistance short occurs with the resultant smell, smoke, flame, noise and explosion. Not exactly the best capacitor behaviour whilst airborne!!! Modern day tantalum capacitors have inbuilt failure suppression, however, this wasn't the case in the 1960s.