You can buy a Senior Railcard in advance online, up to 2 weeks before your 60th birthday, but it will only be valid for travel from your birthday onwards. You cannot buy in advance of your 60th birthday at a station.
Before you apply, you will need a valid form of ID such as a Passport, UK Driving License or EEA National Identity card with you to prove your age. Don’t take it personally, there are lots of you out there that look younger than your years (please tell us your secrets)!
You can apply online or at a staffed station ticket office. If you register for an online account, you can renew again and again without needing to verify yourself – it’s smooth sailing from there. Take a look at Where To Buy.