Well not really furniture but mirror to be exact… I picked up a large wooden framed mirror, nice frame but a horrible orangey stain/varnish on it.

I want a nice dark mahogany colour so thought there was nothing more to it than rubbing it down and staining it. Anyway, sanded it all down, back to bare (very pale) wood and tried to stain it with wood stain but it didn’t really take to the wood at all – it wasn’t absorbed by the grain and had very little impact on the colour. I’ve tried a dark varnish and similar – it hardly changed the colour, a few shades darker but certainly not “dark mahogany” as on the tin.

Any suggestions as to what to try?

These colourd varnishes all seem naff.. I always found the best to be the small bottled stains then when you get the colout you’re pleased with.. a clear varnish.

(although I just completely ruined a pair of gate I made by using naff coloured varnish) 😳

Yup, tried the tin of stain first before trying coloured varnish 🙁

It may be that the previous finish has been drawn fairly deep into the timber and is repelling the new finish and they are incompatible finishes.
It’s hard to say without looking at it but I suppose a coloured varnish is the thing to go for, perhaps even adding some compatible pigment to bring the colour darker.
You want a finish that’ll sit on top of the wood, not a true stain which the wood draws in.

Yeah, that makes sense with the stain being repelled by the old finish.

But why didn’t the 4 coats of coloured varnish make much difference? Just crappy varnish?

Maybe just too subtle a tone.
Depending on whether your varnish is oil, spirit or water based, you could try darkening it down. Use artists oils for oil-based varnish and you can use artists acrylics for water-based varnish.

Go steady as there is a fine balance beween adding enough pigment to darken your varnish, and making the varnish cloudy. It is translucent after all and so adding too much of a pigment may make it cloudy.

Building up your coats is the only way I’m afraid. Failing that, paint it wood coloured and varnish over it, or get someone to make you a frame in Walnut/Sapele/Mahogany…

Good luck.