As long as the hole in the sink is the same size, yes. Sink holes have been pretty standard for some time so it should be OK. But the only way, unless you can get to it from underneath, is to take the old tap out..
The horseshoe flange screws up on a threaded rod over the edges of the hole. Best to fit the pipes into the new tap before you put it in but it can make fitting the flange fiddly. There may be a requirement from your Local Authority to fit isolating valves, you'll need to check. Cheers
[Another] Ossie
January 2010