Audi A3 1.6 Fuel Gauge Issue

Borbon

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Hi all,
Just joined up as looks like a very useful forum!
My GF has just bought an Audi a3, 1.6 2001.
The fuel gauge however is proving faulty, and is showing that the car has way over a full tank of fuel (when it hasnt)
If the ignition is turned off, the gauge will happily go back to empty, but as soon as the key is turned again, it pings back up to full!
When we went to buy the car it was on quater of a tank, so im assuming this is a intermittent problem.

Is this likely the fuel gauge sender in the tank?

Any help would be greatful,
Matt