It's illegal in the United Kingdom to supply alcohol to people who are under 18.
Your use of Paypal will assist here, as Paypal have a minimum age limit:
A Special Note about Children: Children are not eligible to use PayPal Services and we ask that minors (persons under the age of 18) do not submit any personal information to us or use the PayPal Services.
However, this does not appear to be sufficient to satisfy Section 146 of the Licensing Act, because you have to take all reasonable steps to establish the purchaser's age, and that means that you have to ask for evidence. Note the and at the end of 146(4)(a):
Sale of alcohol to children
Where a person is charged with an offence under this section by reason of his own conduct it is a defence that—
(a) he believed that the individual was aged 18 or over, and
(i) he had taken all reasonable steps to establish the individual’s age, or
(ii) nobody could reasonably have suspected from the individual’s appearance that he was aged under 18.
For the purposes of subsection (4), a person is treated as having taken all reasonable steps to establish an individual’s age if—
(a) he asked the individual for evidence of his age, and
(b) the evidence would have convinced a reasonable person.
To satisfy this requirement, I believe it will be necessary to ask the purchaser for evidence of age, since that is the reasonable step required by 146(5) and 146(4)(b)(ii) cannot apply to a website.
If you were accepting payments yourself rather than relying on a third party, then evidence of a credit card would probably be sufficient. But a Paypal account can be linked to a debit card, and those are available to under-18s.
Some jurisdictions abroad have a minimum age of 21 for the supply of alcohol, and you will need to decide how to deal with that.
One way to do all of this might be to use the UK Government's driving licence service which allows holders of driving licences to freely generate and give you a code to check their driving licence. [Purchasers generate the code at that link; check it at another point]. Most driving licence categories expire the day before the holder's 70th birthday, so you can work out how old they are. Once you have this proof of age, you could store it so the purchaser only has to go through the hoop once. A scan of photograph of a licence or passport would also suffice.
As WBT has commented, you need the correct licences to supply alcohol in the first place, but you asked specifically about payments.