Many local authorities in the UK offer recycling collection for aerosols, including kerbside collection.
While not totally plastic-free, for items like deodorant, swapping to an aerosol deodorant might be a good way to reduce your plastic waste.
Many plastic-free deodorants, while they may be better for your health, are often more expensive or have a high upfront cost. Switching to a container which is at least recyclable might be a good affordable option.
Aerosols are made from either tinplated steel or aluminium. They should be completely empty before recycling and any lids should be removed.
Try to find a 'compressed' aerosol option to reduce CO2 emissions.
And look for designs that don't have a separate plastic lid - or if they do take these to your local LUSH store for recycling.