I need to check a 3kw x 27" immersion heater element to see if it's
working.
If I connect my multi meter across the terminals, what resistance should I
find?

The power dissipated in a resistive element is :-

Power = ( V * V ) / R, so transposing the equation we get R = ( V * V ) / P.

So, if the mains voltage is 240V and the power is 3KW the resistance should
be

(240 * 240) / 3000 = 19.2 ohms.

I have done a quick check on this using my electric kettle, which incidently
is 2.4KW , and reads 25 ohms on my multimeter, near enough ?

Ian.