Cornwall or the Lake District could well end up costing more than going abroad.
Obviously it depends on where you stay and what you do, wherever you go, but those places are both expensive for accommodation, eating out, activities etc, unless you just go for walks/the beach etc. Plus if the weather isn't good, you'll likely end up spending more in indoor activities, or staying in the accommodation, doing pretty much what you can do at home, for free.
If you can afford to go abroad, do that. If not, look at doing something that will be cheaper so a couple of nights in a hotel for a city break or a few days in a less overpriced part of the UK.
Cornwall/Lakes seems to be the worst of both worlds. Lovely parts of the world, but expensive without guaranteed sun, and will be a bit shit if weather is typically English, which it could well be, just like now - glorious sun for weeks on end, and now it's going to break just in time for the Easter weekend