Page 133 - Practical English Usage 3ed - Michael Swan, Oxford

can and could (4): interpersonal uses (permission, requests etc) 124
We also use could to ask for permission; it is more polite or formal than can. We do not use could to give or refuse permission (it suggests respect, so is more natural in asking for permission than in giving it.)
Could I ask you something?.... Yes, ofcourse you can. (NOT ••• Bje6f:trse }'6f:t e6ftld.)
May and might are also used to ask and give permission (see 340). They are more formal than can/could. Some people consider them more 'correct', but in fact can and could are normally preferred in informal educated usage.
2 talking about permission: Can everybody park here?
Can and could are also used to talk .about permission that has already been given or refused, and about things that are (not) allowed by rules and laws. (Note that may is not normally used to talk about rules and laws - see 340.3.)
She said I could come as often as I liked.
Can everybody park here? (NOT May ef:lerybody park here?)
3 past: could is not always possible
In talking about the past, we use could to say that somebody had permission to do something at any time ('general permission'), but we do not use could to talk about permission for one particular action in the past. Compare:
When I was a child, I could watch TV whenever I wanted to.
Yesterday evening, Peter was allowed to watch TVfor an hour. (NOT ••• Peter
e6f:tid wateh TVJiJr an hof:tr.)
But could not can be used to talk about one particular action.
Peter couldn't watch TV yesterday because he was naughty.
(The difference between could and was/ were allowed is similar to the difference between could and was/were able- see 122.5.)
4 could = 'would be allowed'
Could has a conditional use (= would be allowed). He could borrow my car ifhe asked.
Could have + past participle means 'would have been allowed'. I could have kissed her ifI'd wanted to.
S offers
We often use can when we offer to do things for people.
Can I carry your bag? ( =Would you like me to ...)",Oh, thank you.
I can baby-sit for you this evening ifyou like.....No, it's all right, thanks.
Could is possible if we want an offer to sound less definite. I could mend your bicycle for you, if that would help.
6 requests, orders and suggestions
We can use can and could to ask or tell people to do things. Could is more polite, more formal or less definite, and is often used for making suggestions.
Can you put the children to bed?
Could you lend me five pounds until tomorrow?
Do you think you could help me for a few minutes?
When you've finished the washing-up you can clean the kitchen. Then you
could iron the clothes, ifyou like.
If you haven't got anything to do you could sort out your photos. ~
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