Is there power to the socket you plug these lamps into? Check by plugging in another appliance that you know to be working.
Is the fuse in the plug ok? Replace temporarily with a 13A fuse to check. Fit a known-good fuse of the correct rating.
Are the lamps OK ? - probably yes because you've already replaced them.
Is the wiring in the plug properly fitted? - sometimes a wire pulls out because the screw was not tightened fully.
Do these two lamps share a single plug and socket? Do they share a mains cable or switch? If they both failed at the same time then it's most likely a common cause.
Fuse-Plug Wiring-No power to socket-Broken Switch- Damaged Cable - or - all your halogen lamps are defective - I hope not.
Richard Buxton, September 2008