You can't beat a night at the bingo, if you have one local.
Sounds shit, but it really occupies your mind and gets the adrenaline pumping. Plus, you might win! (Well, OK, probably not, but if you're skint already the prospect of a windfall will do wonders for the imagination).
A town centre cruise of the charity shops with a cheap café coffee in between stops would kill an afternoon quite pleasantly, unless your local charity shops have done that thing where they believe they are upmarket vintage boutiques and put their prices up. My sister and I regularly kill a whole Saturday afternoon doing the charity shop circuit, and have found that imaginary spending is almost as therapeutic as real spending.
Video/DVD rental. (Does that even exist any more?)
Near where I live is an all-you-can-eat Chinese buffet restaurant for £9.99. Obviously, you could only drink tapwater to go with it on that budget (which they are legally obliged to serve btw) but if you starved yourself beforehand and really took your time, you could get quite an evening out of it. Google to see if you have a local equivalent.
You could definitely get a decent meal and pint at your local Wetherspoons for less than a tenner. Check what days they have what menus, then rock up and relax. Plus the motley assortment of outcasts that drink in 'spoons pubs make for interesting people-watching.
Do you know any drug dealers? Ecstasy is around £2-£3 a pill and will liven up an evening at home, especially with sexytime.
OK, that last one won't be to everyone's liking.
Also, for a tenner each, you could afford a decent meal and some cheap booze from your local Lidl. I once fed two people for a week on a tenner at Lidl, and know from experience that you can get some amazing meals for that money if you 'splurge'.
Walks are definitely good, but the trouble is you have to walk home again once you've had enough. Unless you spend your £20 between the two of you on some beer at a pub at the end of your walk, then a taxi-fare home.
If you're going out in the day time, have you looked into your local bus-service? Many do a cheap all-day ticket, and (if you planned with timetables) you could take a packed lunch on a bus-tour of local places. Without knowing where you live, it's impossible to say whether this would be worthwhile, but in my hometown I am within striking distance of several very nice rural areas and villages.
Do you have a local pick-your-own farm? Fills an afternoon and you end up with loads of cheap fruit with which to make pies, puddings and crumbles at home.
I can probably think of other cheapo activities, but these would be my starting points on that sort of budget. (although obv these reflect my personal inclinations).