I have a 23mo, who has three days at nursery, and a 4.7 yo, who is in reception.
We don't have much of a routine, except that every night, usually after tea we do reading practise with DD1, and I or DH will read some books to them, and usually DD2 will recognise a few letters from that, so we might ask her some more. Often DD2 will get tired quite early, so she goes to bed about an hour before DD1, in which case we usually spend that time doing a workbook, writing letters, playing with her toys or on reading eggs, playing with coins, etc. This is all what the DDs ask to do - in DD2s case I'm not too keen on her learning her letters too early, but she is doing it of her own accord by copying DD1.
We also have started having a thing on Sunday evenings, where every member of the family (including me and DH) takes a turn at reading aloud and telling everyone something interesting. This ranges from DD2 telling us that a C is the start of cat and that a cat says meow (or, as she says it, "cuh dere, cat, meow!") to DH telling us that 98% of adoptees in China are adults or whatever. Reading aloud by me and DH is a poem or a picture book, and for DD1 it is a reading book.
We have a box file that I put colouring sheets, puzzle sheets and so on in, for the girls to pick from when they fancy, and we always run out of puzzle sheets first, as DD1 whizzes through them. She also has taken to sleeping with a calculator on her pillow, and a pen and paper by her bed. 
Me and DH also study, so often if we want to study, the DDs will sit and do puzzle books or colour in. Then of course the day to day stuff of talking about life and involing them in adult conversations, etc.
When they were younger, the plan was to HE, so I tried to do a bit of sitting down work each day, but it varied as to when and what it was (obviously DD2 didn't do this when she was tiny, she usually just had a cuddle and a bf while I helped DD1). Again, it was more going with the flow, although sometimes I would persuade DD1 to come for a walk by giving her a sheet from nature detectives. The child is a bit of a bookish geek, tbh 
I think there is a bit of an "anti learning" feeling, where people assume that learning isn't fun, but imo it is just part of the day. We do plenty of other stuff, and I try and make sure the DDs can amuse themselves too, but like someone upthread said, they are doing play based actvities at nursery and school, and they can get a bit overwhelmed, so they like to do something quiet and challenging at home.
As adults, we wouldn't go a day without reading, writing and leanring something, whether that is researching something that interests us, watching a documentary or the news and chatting about it, or more formal learning, so I don't see why a child, who is made for learning, wouldn't want to do it.
But then I think we might be an odd family...