tl;dr - the NHS is using "accurx.thirdparty.nhs.uk/r/" to send out invitations to book Covid-19 vaccines and the link is genuine. At the end of that link you'll have your own 10 digit unique code (don't share that publicly).
https://accurx.thirdparty.nhs.uk/r/ - enter the 10 digit code you receive in your text message, book your vaccination - get injected and protected, not infected :) Continue to be careful afterwards as you can still get Covid-19 though it is likely to be less severe and I think you can still transmit even if you're not affected.