I have bought a new ignition barrel and switch for my Defender 90 1990. It has a 3.1 Isuzu in it. The old ignition switch is a Lucas, whereas the new one is from Bearmach and I connected it as it was to the Lucas and it's wrong. Could you point me in the right direction? I have three wires: big brown with large spade, big white, and red and white. There is also a brown and red but that wasn't connected My new ignition switch is the one attached.

The old lucas is also attached

Welcome to LZ.

Cheers

Easiest way would be to use a meter and check which contacts connect to what at each of the positions on your existing switch and then check that the new switch operates the same way.
The trouble is that different models use different switches and if your vehicle has had the switch changed at some point (to suit the different engine possibly) then how do you know you have bought the correct replacement?

Although probably not relevant to this query, a perfect example of the differences in ignition switches is in the glow-plug operation.
On early vehicles the glow-plugs were operated by manually holding the switch in the "heat" position for however long was required however on later models this was done automatically by the timer relay so there was no need to hold the switch in that position.

When I changed mine the wires swapped over fine. You sure you haven't made a mistake somewhere>?

From my 1997 110 hard top. The positioning on the switch might be different but here is a chart I made up with the color codes which in theory should be the same.
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The old one you have matches mine. Its not difficult at all if you know how to use a digital multi-meter with continuity.