I think the key thing is probably to carefully combine staples with nice things in a way that looks like the staples are to go with the nice things.
So several individual packets of crackers, some nice waxed cheeses (if they wouldn't mind that they had been posted - I wouldn't, some would). Lidl do great potted pates that don't need to be kept in the fridge - feels more special than tinned ham. You could add a jar of chutney and a half size bottle of wine so that section feels like a "cheese and wine" section - even if in reality it has quite a lot more crackers than would naturally come with a hamper. You could add some cheese biscuits or some cheese straws etc as well.
That would probably set you back £20-£25 if you maxed out on it.
M and S Gold teabags are a relatively big box but nice and inexpensive. They also do really nice, but not super expensive, packets of biscuits - so could do their Viennese finger and other bits which would be a real treat but you could definitely put a few packets in. Add in a packet of their super chocolatey shortbreads or similar for a top treat - or their Swiss rolls are really nice and last a few weeks I think (I like the strawberries and cream and the triple chocolate best).
This is maybe £15-£20 depending how much you buy and forms a kind of "tea and cake" section.
So you could have done those two, then add in your classic Christmas bits: a Christmas cake, an individual sticky toffee pudding, a box of chocs.
Finally, if they have a favourite cuisine, you might be able to do some bits that would go nicely to jazz up other cooking they're going to do - so if it's Italian it might be nice olive oil, a jar of sun-dried tomatoes, one of the magic belazu sun-dried tomato pastes or some Bomba tomato puree, some pitted dried olives or whatever.
Or if it's traditional British stuff, maybe some dried mushrooms would be useful (they're annoyingly expensive), and some pickled walnuts, some Worcestershire sauce, a load of dried bay leaves.
Or whatever cuisine they actually like.
It's not going to be able to be a parcel of staples without looking like a parcel of staples. But you can do a decent number of calories and nice foods and ways that they can make their budget they do have stretcher further without it seeming like a food parcel.