It's a bizarre rule quite frankly, and I've never heard of anyone except Tesco enforcing it...
Out of interest and because there's nothing good on telly I've just checked the T&Cs of some online delivery services, and there's quite a variation! Which is frustrating because there's obviously no hard & fast rule, the supermarkets are just watching their own backs.
Essentially, Tesco, Asda, & Morrisons all have a 'check 25' policy, so OP you may do well to avoid them going forward if you have no proof of ID. Sainsburys & Waitrose require someone aged over 18 to receive delivery. Ocado really don't care, and will leave it unattended so long as you're happy to waiver your rights with regards damage.
Time to change shops! I recommend Sainsburys personally, they're always on time, accurate, and once when they did made a mistake they sorted it straight away (they delivered a bloody massive piece of gammon that was twice the price of the one I'd ordered - I rang and they refunded it on the spot, so got it for free!).
Full T&Cs below...
Sainsburys 'You or someone aged 18 or over on your behalf must be available to receive, inspect and sign for your grocery order.'
Tesco: 'All goods must be signed for on delivery by an adult aged 18 years or over. Tesco follows a "Think 25" policy, so if the person receiving the goods looks under 25, proof of age will be requested. If proof is not available and there is no-one of that age at the address when delivery is being made, the goods may be retained by the driver. '
Asda: 'If there is no one at the delivery address who is aged 18 years or over, we'll leave notification of our visit and return the goods to our store. We will then contact you to arrange redelivery at a convenient time. You may have to pay another delivery charge for this. Customers who are lucky enough not to look 25 or over, will be asked by our driver to provide proof of age to prove that they are 18 years or over. Orders can only be delivered to people over 18 years of age, to ensure that we comply with the laws relating to the sale of age restricted goods.'
Morrisons: 'We will only deliver to somebody who is, in our reasonable opinion, aged 18 or over. Accordingly, when delivering products, if the person accepting the delivery appears to be under the age of 25, we will request photo ID (such as a driving licence or passport) to prove that they are over the age of 18.'
Waitrose: 'Goods must be signed for at the delivery address (or upon collection), by you, or by your nominated representative who must be aged 18 or above. Under no circumstances will goods be left unattended, for example in a garage, or with anybody below the age of 18.'
Ocado: 'You must be 18 years old or over and must have completed the registration process in order to participate in our service.
Ocado will ordinarily only make deliveries when an appropriate person is able to receive the delivery. In the event that you instruct Ocado to leave a delivery unattended at your address Ocado expressly disclaims all liability which may arise by virtue of the delivery being left unattended for a period of time. This includes but is not limited to theft, tampering, contamination and the result of any change in temperature in respect of items which need to be kept chilled or frozen.'