That sounds like a really lovely gift, For that amount including delivery it will be quite tricky as most places have minimum spend or more than £3 delivery - do you have any friends or neighbours who would be willing to help you get things so your nan won't see, or who have Amazon Prime?
There are nice tins of shortbread in christmassy tins for about £10 on Amazon, - things like musical radio tins, or nutcrackers, or books, so there might be a shape there that they would like as a tin, but if you have to pay delivery it will break your budget.
Or Asda, Dunelm and similar places have christmas or pretty themed tins or biscuit barrels which you could order and ask someone to collect for you (or I know Asda put my click and collect santa biscuit barrel in a sealed cardboard box so you could make it a joke with your nan that she's not allowed to know what's in the box, if she's with you, perhaps?) and then sneak extra packs of their favourite biscuits into the normal shopping when she's not looking (or ask someone to buy some and repay them)
The only place I can find at the moment where you would get nice cake and free delivery for that amount is The Cornish Company - and you can pick a delivery date in December - I linked that to the cakes page but they also do fudge and biscuits and they also do 10% off first orders if you sign up - so you might be able to get a couple of really nice cakes delivered - but you could probably get three or four almost as nice loaf cakes at a supermarket for the same price if a friend could help you buy them without your nan knowing!
We often add things to our supermarket shopping/delivery for neighbours and they do for us (we shop at different places so quite often someone will put in our whatsapp group is anyone getting a delivery from xxx and could they please order something) so don't be afraid to ask for help - most people would be happy to help out I think!
To wrap them nicely perhaps cover a box or tin the right size in wrapping paper, or is how to make gift bags from wrapping paper