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Silly question but my poly bulkhead steering bush has a flat side and a domed side. Does the flat side fit towards
the inside of the car?

The bush goes in from the outside in. The flat (thin) side goes in first. If you cut a slot in it it aides in "screwing" it in. Softening it with heat aides this. It has been put in different ways. None of them will make the wheels fall off.

Many thanks, it's been that long since it's had wheels on that the tyres have turned rock hard like Bakelite.

Indeed fit it from the engine bay, but no need to cut into it.
These are the very basic tools I use for the job.
Most important is to make sure that the last bit that needs pressing in is at the top, so it can be reached easily.
That is where the pipe wrench comes in ...

let it sit in some water that has boiled and then some silicone grease and in it pops. Simples

All of the above plus lubricate the bush / steering column with silicone grease otherwise it can suffer from stiction. The thin grease sometimes supplied with other poly bushes dries out.