Why does the signalling power supply in the area not have UPS?
Can't comment specifically about Stretham but with two entirely separate grid supplies and a traction derived supply there is little chance of a total supply failure. If there is no traction derived supply then there is normally no traction supply for trains, so trains won't be running anyway. UPS for signalling supplies require large batteries - for the East London line some years ago the calculations indicated that a UPS to provide 12 hours standby would weigh around 13 tons and would require a room with reinforced floor to house it.
I don't have any details for the design of the supplies at Streatham but a switching system failure and a cable fire, as mentioned in another post, makes me wonder about diversity of cable routes within the compound between the incoming supplies transformers and the switching system.