Sadly the “complete the cycle” inhaler recycling scheme is now closing down, so getting your inhaler recycled is more difficult. A smaller recycling scheme is run by Teva in association with Terracycle (scroll down on the link to see map of pharmacies).
The plastic and aluminium will be recycled, and more importantly any left over propellant gas is captured.
Don’t put your inhaler in kerbside recycling – it will not be recycled.
If you don’t have any facilities nearby to recycle your inhaler, it is still well worth taking metered dose inhalers back to your pharmacy. The inhaler will be incinerated in medical waste, which is a surprisingly good way to dispose of them. The damaging propellants are broken down by the high temperatures into other products which are far less powerful greenhouse gases. More details available here on the recycle now site.